Antoine Semenyo and Omar Marmoush both struck from Foden passes in the first half before Savinho added a late third as City kept their slender title hopes alive at the Etihad Stadium on Wednesday (Thursday AEST).
With both title challengers having two games remaining, City do still have a chance of securing a seventh league crown in nine years.
Yet after Pep Guardiola made six changes and, with the game played in a subdued atmosphere, there appeared an acceptance the odds were heavily against them and focus had shifted to their FA Cup final.
City arguably benefited from facing a Palace side whose eyes may already be on the Conference League final. On this evidence, however, they can expect few favours when the Eagles play Arsenal next.
After two seasons of struggles with form and fitness, there was ample evidence of why the club are prepared to offer Foden, who was making his first Premier League start in more than two months, a new contract.
His selection however, while Erling Haaland, Rayan Cherki and Jeremy Doku were among the substitutes, indicated Guardiola was looking ahead to Saturday's Wembley clash with Chelsea.
City were slow to get going and Palace thought they had scored in the second minute.
Jean-Philippe Mateta's shot looked to have crossed the line before Gianluigi Donnarumma clawed away but Brennan Johnson was ruled offside in the build-up.
Yeremy Pino also had an effort deflected narrowly wide and Chris Richards headed over from the resulting corner.
Foden then took centre stage as he played Semenyo in on goal with a clever backheel. The Ghana international finished clinically.
Tyrick Mitchell tested Donnarumma but Marmoush made no mistake after 39 minutes, turning and firing past Dean Henderson after Foden brought down a high ball in the area.
Foden almost set up another when he crossed for the fit-again Josko Gvardiol, but Henderson saved his header.
Palace rallied after the break as Ismaila Sarr shot at Donnarumma and Jorgen Strand Larsen blazed over.
But the visitors were unable to trouble City regularly and substitute Cherki combined with Savinho to wrap up the scoring, six minutes from time.
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