Two goals by Crystal Palace forward Christian Benteke, who Liverpool sold to their opponents earlier this season, cost the hosts the chance to put pressure on the Premier League's top two with a rare home defeat on Sunday.
Benteke struck late in each half to seal the points and ease the pressure on lowly Palace after Philippe Coutinho had put Liverpool ahead in the 24th minute with a direct free kick.
The home side dominated but conceded an equaliser just before halftime when Benteke, sold by Juergen Klopp in August, scored from a cross by Yohan Cabaye. In the 74th minute the Belgian stooped to head in a corner and win the game.
Klopp's team stay third but are five points behind second-placed Tottenham Hotspur having played two games more. More worryingly, Manchester City and United are respectively two and three points behind Liverpool with two games in hand.
Palace moved up four places to 12th and should now be safe from relegation after a sixth win in eight games has taken them seven points away from the drop zone.
"I was motivated, I would say," Benteke told Sky Sports.
"We knew it was going to be hard to play against them, but I give all the praise to the lads for the hard work.
"I respect Liverpool but what happened here is behind me."
Palace manager Sam Allardyce has brought about a transformation since replacing Alan Pardew, who was sacked in December with the London club a point above the bottom three.
"I can breathe a little easier," Allardyce told Sky Sports.
"We have five games to go so this one is so important.
"I think the key was tactical. They (Liverpool) have lost six goals on corners. They use a zonal system and don't mark men. If you get on the move you may get a chance."
Allardyce may have tightened up Palace's defence but, as he suggested, Liverpool's rearguard, having conceded more goals than any of the other leading clubs, looked vulnerable again.
"I know what everybody's saying but we have to bounce back," Klopp said.
"If we want to go to the Champions League we have to win the last games.
"Crystal Palace are a good side but we dominated the game. It's really harsh, really frustrating."
Liverpool do not play again until May 1, away to Watford, by which time Manchester City and Manchester United will both have played twice and could have pushed them out of the top four.