Parker’s side, who took just one point from their first seven games this season, are now level on points with 17th-placed Brighton and in the bottom three on goal difference alone.
Scott Parker made two changes from the side which dominated but failed to score against Crystal Palace last weekend; Ruben Loftus-Cheek dropped to the bench as the west Londoners looked to Ademola Lookman and Bobby Decordova-Reid to trouble a fragile Liverpool with their pace. And they did just that.
Harrison Reed and Lemina were aggressive in midfield, while Lookman twice raced in behind down the left only to fire wide the first time before seeing a second attempt deflected over the bar.
They had to remain alert at the back. Mohamed Salah was smothered by Alphonse Areola after Liverpool pounced on a loose ball before spinning and firing over from the edge of the area. Xherdan Shaqiri also found the top of the net with a dipping free-kick.
But it was Parker’s side with the initiative and fight. They looked to be left ruing more missed chances heading into the break before Lemina struck in the final minute of the first half.
The Gabon international, who is on loan from Southampton and will join permanently if Fulham beat the drop, barged his way past Salah to win the second ball from a free-kick before firing a low effort perfectly into the far corner - nothing less than the visitors deserved.
Liverpool responded quickly after the restart, Areola pulling off a wonderful save to deny Diogo Jota’s fierce volley while Jurgen Klopp sent Sadio Mane on just after the hour mark.
Parker knew what was coming and, with Liverpool controlling the ball but yet to create much, the Fulham manager sent on Loftus-Cheek for striker Josh Maja to protect their lead.
Liverpool toiled, Shaqiri bent a shot wide of Areola’s goal but could not find a leveller as the Frenchman, with Tosin Adarabioyo and Joachim Anderson ahead, dealt with anything which came their way.
Newcastle are Fulham’s closest rivals at the bottom. Brighton dropped more points again on Saturday but should have the quality to beat the drop, while Steve Bruce is presiding over bust-ups and turgid football, as displayed in their 0-0 draw with West Brom.
As the Magpies fight fires, Parker has never given up and has everyone onside.
"Scott Parker knows how to make the players feel good, to feel confident,” said Frank Zambo Anguissa in the Observer on Sunday morning. “He always finds the words to get through to us. If he tells you it’s possible, you believe it’s possible."
Fulham are hard to beat at the back - Liverpool have shipped more goals this season - and are attractive to watch going forward.
The Cottagers host Newcastle, who sit one point ahead with a game in hand, on the final day of the season. Parker will be under no illusions that this season will go to the wire.
The former midfielder has done a wonderful job in west London since being parachuted in with their relegation all but confirmed two seasons ago. For a Newcastle side offering the football on show this weekend to stay up ahead of a Fulham squad who have battled back from a woeful start with a fine mix of grit and glamorous football would be a travesty.
Parker will simply hope that their poor start does not, eventually, undermine everything which followed.