Mohamed Salah scored his 200th goal for Liverpool before Harvey Elliott's last-gasp winner sealed a dramatic 2-1 victory against Crystal Palace that sent the Reds to the top of the Premier League on Saturday.
Jurgen Klopp's side were in danger of a damaging defeat in the title race after Jean-Philippe Mateta's penalty put Palace ahead in the second half at Selhurst Park.
Unbelievable scenes as Liverpool take the lead against Crystal Palace 😲
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But Palace's Jordan Ayew was sent off with 15 minutes left and Liverpool took full advantage to erase a previously spluttering performance with a blistering finale.
Salah's 14th goal this term made him the fifth player to score 200 for Liverpool in all competitions after Ian Rush (346), Roger Hunt (285), Gordon Hodgson (241) and Billy Liddell (228).
In his 247th Premier League appearance, the Egypt star also reached 150 goals in the competition, including two scored for Chelsea, putting him in the all-time top-10 list level alongside Michael Owen.
Despite Salah's landmark, a point would have been a disappointing result for Liverpool, but young midfielder Elliott came off the bench to seal the points in stoppage time.
Liverpool's third successive league win moved them one point above second-placed Arsenal ahead of the Gunners' trip to third-placed Aston Villa later on Saturday.
With home games against Manchester United and Arsenal looming before Christmas, the Reds have a golden opportunity to cement their title credentials heading into the new year.
Klopp had called a television presenter "ignorant" for joking that the 1230 GMT Saturday kick-off was the German's "favourite" time to play.
The Reds boss has made a habit of complaining about the schedule whenever Liverpool have a match in the early Saturday slot after playing the previous Wednesday.
Liverpool leave it late
Initially, it seemed Klopp's dislike for the kick-off time would be renewed as Liverpool struggled to find any rhythm in wet and windy conditions in south London.
Liverpool were fortunate not to fall behind when Jefferson Lerma's close-range effort forced a superb save from Alisson Becker, with the rebound hitting the post before it was hacked off the line by Trent Alexander-Arnold.
Palace were awarded a penalty when Odsonne Edouard was bundled over Virgil van Dijk, but Will Hughes had clearly fouled Wataru Endo before passing to the forward.
Referee Andy Madley was told to consult the pitchside monitor and overturned his penalty decision.
For the first time in the league this season, Klopp's side failed to muster a single shot on target in a dismal first-half display that ended fittingly with Alexander-Arnold misplacing a simple pass.
Palace deservedly took the lead in the 57th minute as Jarell Quansah's challenge on Mateta was deemed worthy of a penalty after Madley checked the monitor.
To Klopp's bewilderment, VAR only intervened to prompt the decision several moments after the foul.
Liverpool were furious but Mateta was unfazed, barely taking a run-up as he dispatched the spot-kick past Alisson with ease.
But luck was on Liverpool's side as Palace forward Ayew was dismissed for a soft second booking in the 75th minute and within 60 seconds the visitors were level.
If the sending off had an element of good fortune for Liverpool, there was more to come as Cody Gakpo's cross was only cleared to Salah, whose shot from 10 yards took a wicked deflection as it flashed past wrong-footed keeper Sam Johnstone.
Liverpool finally had some momentum and their late siege produced a winner in the first minute of stoppage time.
Elliott took possession 30 yards from goal and swerved away from his marker before unleashing a superb strike that beat Palace substitute keeper Remi Matthews at his near post.
In the final seconds, Alisson had to save from Joachim Andersen to preserve Liverpool's hard-fought success.
AFP