Liverpool were seemingly coasting to victory and a three-point lead over Manchester City at the top of the Premier League with goals from Joe Allen, Daniel Sturridge and Luis Suarez.
But Palace stormed back with three late goals, with substitute Dwight Gayle scoring twice after Damien Delaney put Palace back in the game with a screamer in the 79th minute.
Liverpool's title hopes, already receding after last week's loss to Chelsea, are now hanging by an even more slender thread.
They have 81 points with one match to play while City have 80 points and two games to go plus a nine-goal better goal difference than Liverpool.
City host Aston Villa on Wednesday and West Ham United on Sunday while Liverpool's remaining game is at home to Newcastle United on Sunday.
Liverpool's players slumped to the ground at the end after allowing Palace back into the game that seemed all over with just 11 minutes of normal time to play.
Goals from Allen after 18 minutes, Sturridge after 53 minutes and newly-crowned Footballer of the Year Suarez two minutes later put Liverpool into a commanding position.
Wales international midfielder Allen put Liverpool ahead when he was left unmarked following a Steven Gerrard corner and headed in for his first Premier League goal for Liverpool in his 50th league appearance for them.
Sturridge doubled the score with his 21st goal of the season with a low deflected shot eight minutes into the second half while Suarez scored his 31st goal of the season two minutes later after playing a swift one-two with Raheem Sterling to take Liverpool's goal tally this season to 99 goals.
But as has happened so often this season, Liverpool's defending cost them.
Liverpool continued to pour forward in a bid to further trim Manchester City's goal difference advantage but paid a heavy price for leaving themselves exposed to the counter-attack.
Delaney reduced the arrears with a fierce shot before Gayle brought Palace right back into the game after Yannick Bolasie, a continual threat on the break squared back to him and he swept the ball home.
The third goal came after a long ball forward and Gayle took advantage of more poor defending to equalise and complete an incredible fightback by the home side.
