Diogo Jota rescued ten-man Wolves with an injury-time equaliser in a dramatic finale to ease the strain on manager Nuno Espirito Santo.
Santo had been heading for a fourth defeat in a row as Wolves manager for the first time since he took the job, as their struggle to balance Europe and the Premier League continued.
In the end, though, it was Roy Hodgson who was smashing his hand into a chair after his Crystal Palace team were stunned at the death.
Goals at Selhurst Park have been in short supply but Palace had got their noses in front with Leander Dendoncker’s own goal early in the second half.
Romain Saiss’s 72nd-minute dismissal, after his second yellow card, left Wolves with an even tougher task, but they somehow summoned a last-ditch effort to salvage a point.
Joel Ward was a guilty man as he failed to clear the danger at the death.
Wolves have won six out of seven in Europe - but have now drawn four and lost two of their six Premier League games.
They went into this game after successive losses against Everton and Chelsea in the league and, more recently, Braga in the Europa League on Thursday.
Nuno’s eagerness to stop the rot was shown by the fact he started the game by reverting back to a 3-4-3, in place of 3-5-2.
Wolves enjoyed an early spell of possession and caused Palace a scare when Dendocker's shot was blocked by James McArthur.
Palace were struggling to break out of their own half but, when they did, Wilfried Zaha was predictably the danger man.
Hodgson’s team forced Rui Patricio into a save when Jordan Ayew headed at him from Luka Milivojevic’s corner.
There was then a more spectacular save at the other end from Vicente Guaita - leaping and flinging out his right hand - to keep out Matt Doherty’s header inside the six-yard box.
Although the sides went into the break level at 0-0, Wolves had looked the more threatening side, but they were soon to pay for not making it count.
Palace needed to offer more in the second half and straight away, Jeffrey Schlupp provided a spark, dashing down the left and into the penalty area before crossing - and Wolves failed to clear the danger.
McArthur eventually laid the ball off for Joel Ward, who struck from 20 yards and found the net, with the help of a deflection off Dendoncker.
Ward - who rarely scores - was screaming in delight, but the goal was eventually judged, cruelly but correctly, as an own goal.
Having gone ahead, Palace suddenly found another gear and that was the cue for Nuno to change his tactics again and bring on Ruben Neves in a familiar 3-5-2.
Saiss did damage to their hopes though when, already booked, he inadvisedly brought down Zaha and was sent off.
Substitute Christian Benteke and Schlupp had chances to add to the lead but both shot straight at Patricio.
The game still looked safe for Palace, with Adama Traore firing a deflected effort wide for tiring Wolves.
A twist in the tale was to come though as Traore’s cross was not cleared by Ward - who suddenly became the villain - and Jota struck.