Goals either side of half-time from Glenn Murray - his fifth in as many matches - and Jason Puncheon sealed all three points for Palace, with Yaya Toure's thumping late drive proving scant consolation for the champions.
Manuel Pellegrini's side now sit nine points adrift of Chelsea having played a game more, and they head into Sunday's derby with Manchester United in fourth and a point behind their rivals having lost three of their last five league fixtures.
City felt Murray's first-half opener should not have stood, claiming that both he and Scott Dann were offside in the build-up, with replays showing the two decisions to be marginal.
But there could be no complaints over Puncheon's free-kick early in the second period, a fine curling effort that left Joe Hart with no chance.
City pressed hard to get back into the game and Toure's rasping shot reduced the arrears with 12 minutes to go, but they could find no way back as Palace's resurgence under Alan Pardew continued.
Martin Kelly for Pape Souare was the hosts' only change from their 2-1 win at Stoke City last time out, and it was the former Liverpool defender’s dangerous cross in the second minute that Wilfried Zaha blazed over from close range when he ought to have scored.
City responded strongly to that early scare and pinned Palace back with a period of constant pressure.
David Silva twice brought smart saves out of Julian Speroni, while Sergio Aguero struck the base of the left-hand upright with the goalkeeper motionless.
Aguero stabbed over as City continued to dominate but then, against the run of play, Palace took the lead in the 34th minute.
Dann got on the end of Joe Ledley's flick and, after his effort was saved by Hart, the ball ran kindly for Murray to tap home from two yards.
City left the field at half-time complaining to the officials about the validity of the goal, and their mood was not improved three minutes after the restart when Puncheon sent a 20-yard free-kick over the wall and into the bottom-right corner.
There was further controversy 20 minutes from time when Murray clearly handled Fernandinho's deflected shot in the area, but referee Michael Oliver waved away City's vociferous appeals for a penalty.
James McArthur did brilliantly to clear another Fernandinho effort over the bar as the visitors piled on the pressure, and Toure's superb left-footed strike from 20 yards raised hopes of a comeback.
City substitute Samir Nasri and Toure both went close with deflected efforts late on but, as was the case for Liverpool last May, City's bid for Premier League glory seemingly came to an end at Selhurst Park.
