Substitute Dwight Gayle's late brace completed a sensational Eagles comeback after Joe Allen, Daniel Sturridge and Luis Suárez struck to put Liverpool three goals to the good.
Damien Delaney's defelcted effort in the 79th minute triggered an astonishing collapse from Brendan Rodgers' side, as players and fans uncontrollably wept at Selhurst Park.
Liverpool are a point ahead of City ahead of the final day of the season, but the Manchester side have a game in hand and boast a vastly superior goal difference.
After Suárez's third, the Reds' followers implored the team to attack, hopeful of reducing the goal difference deficit. Everything seemed to be in order.
Palace have been instilled with a workmanlike attitude under Tony Pulis and, with the backing of a ferocious home crowd, miraculously clawed their way back into the game with 11 minutes remaining.