Christian Benteke scores twice against his former club to lift Crystal Palace up to 12th place and seven points clear of the relegation zone.
His double wiped out a stunning free-kick from Philippe Coutinho.
Liverpool miss chance to tighten their grip on a top four finish.
Jurgen Klopp's side stay in third but are just two points ahead of Manchester City and three clear of Manchester United.
Both Manchester clubs have two games in hand on the Reds.
What a story. Christian Benteke, sold by Jurgen Klopp last summer, puts a sizeable dent in Liverpool's Champions League hopes. Palace move onto 38 points - which should be enough to secure them Premier League football for another season.
Full-time: Liverpool 1-2 Crystal Palace
Trend Alexander-Arnold tries to swing a cross in but it veers out of play before Hennessey pulls it out of the air. That should be that...
Liverpool have two minutes to rescue this; Joel Matip has been sent up front.
Liverpool finally breach the Palace defence as Townsend falls asleep. Moreno is freed down the inside left channel, but his cross is dug out. There's an almighty scramble as the corner comes in but Palace manage to hack it away.
SIX MINUTES of injury time added on here.
That's a nasty challenge from Grujic. Tomkins does excellently to dispossess Firmino and bring the ball out of defence before the Serbian dives in to take him out, connecting cleanly with the Palace defender's ankle. Grujic is booked, and Tomkins will need some treatment.
Christian Benteke gets a warm reception from everyone in attendance at Anfield as he is replaced by Fraizer Campbell.
With Palace sitting back, Coutinho can't pick his way through and decides to launch one on goal from 25 yards out. It's a poor effort that veers clean over the bar.
Here's the last of those flurry of changes, Marko Grujic is now on to replace Clyne. Seven minutes plus injury-time remain.
Allardyce responds to those Liverpool changes, here comes Damien Delaney to replace Cabaye.
Andros Townsend is putting a terrific shift in down the right at the moment, he is back to help out his full-back on every occasion. Alberto Moreno has just come on for Milner so his work load might increase even more yet.
Benteke's loves playing against Liverpool.
There's a change for Liverpool too. Dejan Lovren looks to have picked up a knock and he is replaced by Trent Alexander-Arnold.
Big Sam is trying to sure things up a bit with Patrick van Anholt coming on for Zaha.
He's done it again! Benteke is well placed in the box to casually nod home from six yards out but it is more miserable defending from Liverpool. Both Lucas and Matip fail to deal with Townsend's corner as it bounces across the face of the box, with Palace's greatest threat from set pieces standing unmarked in the box. Abysmal defending.
Liverpool 1-2 Crystal Palace (Christian Benteke, 73)
What a chance for Palace! Liverpool can't clear the resulting free kick and a miserable attempt to hack it clear falls to Cabaye, who lashes a wild effort clean over the bar. He only has a split second to get a shot away, but should have done much better there.
Nifty footwork from Zaha who does well initially to hold up the ball before skipping across Clyne. The Palace winger is tripped and Cabaye will whip in the free kick.
Big Sam is absolutely raging with something at the moment. I hope it's not just over the decision to award a throw-in Liverpool's way, because that's what it looked like.
Roberto Firmino should do better there. Milner threads a delightful ball into the box for the Brazilian to run onto, but he opts out of the challenge with Hennessey rushing out to claim the ball. It looked like he could have got there first if he had really wanted to.
Coutinho stands over another free kick out on the right. I've just realised I have started the last three posts here with his name but he's having that sort of game.
Coutinho is bullying Palace defence. Four Palace players can't get near him as he cuts across the face of the box, but the Brazilian can't get his shot away as bodies are thrown across him and the chance goes.
Coutinho gets the ball from Lucas on the edge of the D and brilliantly fools Kelly with a dragback to get the ball back onto his left foot. He has space to shoot, but he hammers his effort over the cross bar.
Schlupp bursts straight through the Liverpool midfield at pace, leaving Lucas for dead before breaking into the box. Lovren steps across but doesn't make a challenge, forcing the Palace full-back to run the ball out of play under pressure.
And we are back underway for the second half at Anfield.
Half-time: Liverpool 1-1 Crystal Palace
Two minutes of time added on at the end of the first-half.
Benteke does it to Liverpool again! The home side are all over the place defensively with Ward's ball over the top down the right pounced upon easily by Cabaye. He forces an inviting ball across the goal with Benteke a yard clear of Matip and drills the ball into the roof of the net. Well-worked by Palace, but Liverpool were sleeping there.
Goal! Liverpool 1-1 Crystal Palace (Christian Benteke, 42)
Christian Benteke goes down in the Liverpool box but the only thing he is getting for that is a yellow card for simulation.
Emre Can gets that all wrong. Really wrong. Milner feeds the ball inside the box, right into the path of the German who is free in the box but his first-time effort is sent wide. Really wide. So wide I think it may have gone out for a throw in.
SHOOT, James! Coutiho does brilliantly on the edge of the box to feed a ball into the pass of the overlapping Milner, who cuts inside across the box shaping to shoot. He takes a second too long to make up his mind however and Tomkins can nick the ball away from him.
Magic from Coutinho; his 10th goal of the season has given Liverpool the lead.
Brilliant from Coutinho! The Brazilian wins a free kick about 25 yards out from goal and he immediately places the ball down to take it himself. His execution is perfect, curling it over the Palace wall and into the top left corner out of Hennessey's reach.
Goal! Liverpool 1-0 Crystal Palace (Philippe Coutinho, 23)
Neat stuff from Benteke. The Belgian receives the ball infield and expertly spins past Lucas. He bundles his way past two meek challenges to reach the edge of the box and looks for the far corner, but can't behind his shot inside the post.
It's been a fairly even contest so far at Anfield.
Liverpool drive forward on the counter attack with Can feeding Coutinho on the edge of the box. He has Milner overlapping to his left and finds him with a backheel. The ball is caught a little behind the full-back who tries to hit a first time cross in towards Origi but can't find the accuracy in it. Liverpool guilty of trying to be a bit too intricate there.
Palace have got a foothold back in this match in the last few minutes with Townsend and Schlupp asking some questions down the left. It's very subdued in Anfield so far.
Again, Liverpool get in down the right side, this time from Firmino who cuts menacingly inside but Tomkins can hack away his cross.
Clyne, playing against his former club, has acres of space to trot into down the right with Andros Townsend abandoning his defensive duties. His cross however is forced out for the first corner of the game.
And we are underway at Anfield.
We are almost ready to get underway at Anfield; the teams are making their way out of the tunnel onto the pitch.
Is there any risk in Joel Matip playing today? Not according to Jurgen Klopp, who was satisfied with what he saw from the Cameroonian in training on Saturday.
"Ragnar Klavan was in training yesterday and felt a little bit still with the medial ligament, but should be OK for next week. Joel yesterday did normal training, so it was clear he could start. The same for Lucas Leiva, he came back. The line-up, I am fine with it."
There is a spot on the Liverpool bench for 17-year-old Rhian Brewster this afternoon. Daniel Sturridge's absence opens up the spot for him on the bench.
Crystal Palace have kept things simple too; with Sam Allardyce making just one enforced change with James Tomkins coming in for the Liverpool-owned Mamadou Sakho.
After all that worry about Liverpool's options at centre-half, Jurgen Klopp is able to name the same side that beat West Brom last time out. Joel Matip partners Dejan Lovren at centre-half with Lucas Leiva also fit enough to keep his spot in midfield.
There's no Daniel Sturridge, he misses out following reports of a hip complaint.
Palace have arrived at Anfield.
Crystal Palace team to face Liverpool: Hennessey, Ward, Tomkins, Kelly, Schlupp, Milivojevic, Cabaye, Puncheon, Zaha, Townsend, Benteke
Subs: Speroni, Van Aanholt, Delaney, McArthur, Flamini, Sako, Campbell
BREAKING: James Tomkins comes into replace Mamadou Sakho, who is isn't eligible to play against his parent club today.
Liverpool team to face Crystal Palace: Mignolet, Clyne, Matip, Lovren, Milner, Lucas, Can, Wijnaldum, Coutinho, Firmino, Origi
Subs: Karius, Gomez, Grujic, Moreno, Brewster, Woodburn, Alexander-Arnold
BREAKING: Joel Matip recovers from injury and is fit enough to partner Dejan Lovren at the heart of defence
It isn't exactly news these days, but Daniel Sturridge is also expected to be ruled out today. The Liverpool Echo report the striker is feeling some discomfort from an old hip injury and while it isn't thought to be serious, he will not be risked today.
Team news: Crystal Palace
Mamadou Sakho has been central to Palace's fightback in the second-half of the season but the France international – who Sam Allardyce is desperate to sign on a permanent deal – is ineligible to face his parent club today.
That absence could prompt a return for James Tomkins at the back. Scott Dann, Connor Wickham and Pape Souare are out.
Joe Gomez to step up today? It's an option for Klopp today.
"We have to find a solution for the weekend, today I don't have to find one for next year. It's not 100% Lucas can't play, it's not 100% Joel can't play, it's not 100% Ragnar can't play, but they are not in training at the moment. So that is not too cool. Joe Gomez did well on Monday, for the Under-23s, and made big steps in the last few weeks so maybe now we have to try this pair [Gomez and Lovren]. We will see, I don't know in this moment."
Team news: Liverpool
Adam Lallana returned to outdoor training this week following his thigh injury suffered during the recent international break. The visit of Sam Allardyce's side comes too soon for him, however, with Klopp not expecting the midfielder to return to full first-team training until Wednesday.
Klopp on Liverpool's defensive injury problems
"There are a few little things from last game which doesn't make it easier. There is a little muscle problem with Joel Matip, a little thing with Lucas Leiva. There is still a problem with Klavan, there was a very, very small medial ligament [problem], very small, but it could mean there is not enough time for Palace."
Team news: Liverpool
Jurgen Klopp has a bit of a defensive crisis on his hands this afternoon. Joel Matip, Ragnar Kavan and Lucas Leiva all missed training this week with knocks. The Liverpool boss may have little alternative but to turn to 19-year-old Joe Gomez to partner Dejan Lovren at the back.
Liverpool's grip on a top four finish is tightening. Trips to Stoke City and West Brom looked like they might pose a threat to those Champions League aspirations, but Jurgen Klopp's side passed those tests with flying colours. The Reds have played more games than fourth place Manchester City and fifth place Manchester United, but a slightly more favourable fixture list bodes well for them.
Crystal Palace boast the third best run of form in the league heading into this afternoon's match and while they aren't quite safe yet, the four point cushion between them and 18th place Swansea City means they are closing in on another season of Premier League football.
Recent victories over Chelsea and Arsenal have ensured plenty of optimism for their trip to Anfield, with Christian Benteke eager to send a message after he was sold by Klopp last summer.
Stick around, all your team is on its way.
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