Brendan Rodgers's men were three goals up midway through the second half but Damien Delaney and two goals from Dwight Gayle handed Manchester City a huge advantage.
Brendan Rodgers's men knew only a victory would suffice at Selhurst Park after City, which now sits one point behind the Reds with a game in hand, edged to a seemingly crucial 3-2 triumph at Everton on Saturday. That result left Manuel Pellegrini's men, who wrap up their season with home games versus Aston Villa and West Ham, at the summit thanks to goal difference.
For large parts of the game against Palace, it appeared merely a question of how much Liverpool could eat into City's nine-goal lead after Daniel Sturridge and Luis Suarez added to Joe Allen's first league goal for the club.
But, after cruising at 3-0, the visitors had to endure a chastening finish as Damien Delaney's deflected 79th-minute strike was immediately added to when Dwight Gayle capped a smart counter attack with a cool finish two minutes later.
|VIEW FROM SELHURST PARK
|By Wayne Veysey
A remarkable encounter at a raucous Selhurst Park ended with substitute Kolo Toure leading off an inconsolable Luis Suarez with his shirt over his face to hide his tears from the world.
Suarez had scored one of Liverpool's goals as Brendan Rodgers's side eased into a convincing three-goal lead and searched for more in an attempt to bridge the goal-difference gap on Manchester City.
But Crystal Palace refused to give in and scored three goals in nine remarkable minutes to produce one of the most unexpected Premier League comebacks ever.
An incredible finish at Palace has left the Reds, which end the season at home against Newcastle on Sunday, hoping that Villa and West Ham can do them favors to revive their hopes of landing a first top-flight title since 1990.
Liverpool began in typically quick fashion and had a strong penalty appeal turned down after Glen Johnson went down under a clumsy challenge from Yannick Bolasie.
Undeterred, the visitors continued to press forward and almost took the lead in the 16th minute. Allen delivered a glorious ball over the center backs but Johnson, having made a fine diagonal run behind Joel Ward, nodded just over the crossbar.
Palace was to rue its failure to heed the lesson from Steven Gerrard's first corner as it conceded via a set piece for the first time under Tony Pulis two minutes later. Allen was the beneficiary of some lackluster defending, marking his 50th league appearance for Liverpool by nodding across Julian Speroni and into the net, having found space at the back post with a clever run.
Jason Puncheon then forced a good save from Simon Mignolet with a powerful effort from distance and the Belgian goalkeeper had to be on a high alert again moments later, producing an even better save when turning Mile Jedinak's thunderbolt over.
Any momentum Pulis's men had built before the break was quickly extinguished after as Liverpool attacked with verve.
Sturridge was the main threat, seeing an effort tipped on to the post by Speroni before strike partner Suarez, rumoured to be playing despite illness and having added the Football Writers' Player of the Year award to the PFA gong earlier in the day, uncharacteristically fired over with the goal gaping.
However, Sturridge doubled the advantage moments later, his deflected effort trickling beyond Speroni. Suarez soon got in on the act, sliding coolly under the goalkeeper following a fine one-two with Raheem Sterling.
Liverpool piled forward with similar intent thereafter yet quickly found itself defending for its life as Palace flipped the narrative.
Delaney was the first to strike, his pot-shot taking a wicked deflection and beating Mignolet. Suddenly Palace had hope, which was only added to as Bolasie surged forward on the break and slid in Gayle - who made no mistake.
And Gayle was not finished, breaking Liverpool hearts with a thunderous left-footed strike after Glenn Murray's chested pass.
Both sides tried for an unlikely winner without avail, meaning Liverpool now requires a City slip-up and victory on Sunday to have any hope of lifting the Premier League title.