Manuel Pellegrini s side were rocked as Glenn Murray s first half goal and Jason Puncheon s excellent free kick immediately after the restart gave Palace the cushion they needed to withstand late pressure after Yaya Toure had given City hope with a 78th minute strike.
City s third successive away league defeat, their fifth loss in their last seven games in all competitions, leaves them languishing in fourth place with Chelsea also having a game in hand on them.
Their predicament was simply summed up by Pellegrini before this game when City s manager admitted his side needed a perfect end to the season and a Chelsea stumble to regain pole position.
Yet while Pellegrini has had his eyes set on tracking down the leaders, the weekend victories for Arsenal and Manchester United confirmed City are now in a testing battle to finish in the top three, which guarantees a place in next season s Champions League group stage
In the circumstances, next weekend s Manchester derby has assumed even more significance than usual.
“For today I m very happy with the way the team played, but I m very disappointed with the score,” Pellegrini said.
“All we can do is try to add the most amount of points we can and we will see who is first, second, third and fourth.”
If City were to avoid becoming the latest side to fall victim to Alan Pardew s rejuvenated Palace team, they would have to maintain high standards at both ends of the pitch.
Sergio Aguero s first half display suggested he was more than capable of providing a cutting edge in front of goal but it was at the back where Pellegrini s side were found wanting.
City have made a habit of conceding costly goals this season with Pellegrini failing to settle on a convincing and consistent back-four.
There was an early sign Palace were capable of troubling the visitors when Martin Kelly s low cross should have been met with a better finish than Wilfried Zaha s skied effort after just two minutes.
But much worse was to come 10 minutes before the end of the first half when Murray made the breakthrough while the visitors appealed for offside.
Prior to that moment, Pellegrini s team had looked in control, with Aguero striking the woodwork with a smart snapshot after creating space on the edge of the Palace area.
That came after the Argentina forward s pace had allowed him to collect Joe Hart s long clearance and set up David Silva, who was denied only by Julian Speroni s excellent save.
But those efforts counted for nothing in the 34th minute when City failed to deal with a clipped ball into the box from Joel Ward after a harmless looking corner had been cleared.
The visitors were convinced first that Scott Dann was offside as he moved onto Ward s ball in and fired a volley that deflected off Hart, and then questioned whether Murray had strayed beyond the defence as he followed in to score from close range.
Referee Michael Oliver and his assistants were unmoved by the protests that continued at the break, with City captain Vincent Kompany continuing to make his feelings known.
It did mean, however, that Palace had a foothold in the game and they have demonstrated impressive tenacity in recent weeks.
It was clear City faced a testing challenge to get back into the game but the task facing them grew even more daunting when Puncheon added the second goal three minutes after the restart.
Once again the visitors did themselves no favours with Fernandinho producing an unnecessary foul to halt Murray just outside his own area, handing Puncheon the opportunity to lift an excellent free-kick over the defensive wall and beyond Hart.
City were convinced they should have had a penalty when Murray appeared to handle and Toure s powerful shot provided them with a late lift but they were unable to find an equaliser.