Palace had taken the lead through Joe Ledley's early second-half goal but a dramatic turnaround saw Jurgen Klopp's side take all three points, with Christian Benteke's winner coming six minutes into injury time.
Pardew forced to alter team due to injuries to Hennessey and Wickham
Alan Pardew made four changes to the side that drew 2-2 with Sunderland in midweek; Alex McCarthy, Ledley, Pape Souare and Emmanuel Adebayor replaced Wayne Hennessey, Jordon Mutch, Martin Kelly and Connor Wickham.
Klopp left star players Daniel Sturridge, Philippe Countinho and Nathaniel Clyne on the bench for Liverpool and gave rare starts to Jon Flanagan and Divock Origi.
Palace signalled their intentions early in the game and pressed Liverpool high up the pitch, counter-acting Klopp's renowned approach to games. Yannick Bolasie, on his return to Selhurst after injury, was a threat throughout the game and he created Palace's first chance of the game when his cross was met by the head of Adebayor, but the striker's header cannoned off the bar when it seemed destined for the back of the net.
Klopp's side grew into the game after Palace's early spell of pressure and McCarthy had to be at his very best to stop Roberto Firmino's low cross reaching Origi. The Belgian youngster then had an effort of his own when he exchanged passes with Emre Can, before curling the ball just over the bar.
Palace take the lead to reignite change in fortunes
The game then grew into life in the second half and Palace took a deserved lead just three minutes after the break. Pinball in the box following a Yohan Cabaye corner eventually fell to Ledley and the Welshman hammered the ball home from 20-yards.
Sending-off swings game in Reds' favour as they spark dramatic comeback
James Milner was sent off shortly after the goal after picking up his second yellow card when he prevented Wilfried Zaha breaking away. However, strangely, the incident swung the game in favour of Liverpool as they changed their formation, brought on Philippe Coutinho, and benefitted from some Palace defending that exemplified the horrendous run that has ensued since the Christmas period.
The reds had hardly troubled McCarthy throughout the game, but that soon changed when the Eagles goalkeeper slipped after receiving a back pass - gifting the ball straight to Firmino, and the Brazilian made no mistake in tapping into the goal in front of a stunned Selhurst crowd.
An end-to-end climax gave the game a nervy sense as both sides had chances to snatch all three points, however, it was Liverpool who had the final say in a scintillating second-half. Benteke - who, like Fabio Borini on Wednesday, had only been on the pitch a matter of minutes - went down in the box under challenge from Damien Delaney and, after a brief consultation with his linesman, referee Andre Marriner pointed to the spot in what was the 95th minute of the game. Benteke dusted himself down and sent McCarthy the wrong way from the spot to condemn Palace to an agonisingly heartbreaking defeat.
Pardew now finds himself under serious pressure to end Palace's fortunes around, but history is beginning to repeat itself as the former Newcastle United boss finds himself in a similar predicament to the one he was in at the Magpies and failed to find results. Although the performance was much better - particularly in the first half - the worrying signs remain as the defensive side of Palace's game is in turmoil. Too many errors are creeping into performances and the season appears to be tumbling into a disastrous state.