Edin Dzeko scored the first goal of a Yaya Toure cross to allow City to take an early lead before the Ivorian himself curled a second goal from 15 yards in the 44th minute of the match, the BBC reports.
Third-placed City now has a game in hand over leaders Liverpool and second-placed Chelsea as well as a superior goal difference.
Toure came back into the team after missing the last two matches with a muscle injury.
Crystal Palace had won their previous five games, a run that began with a 1-0 victory over Chelsea. The 1-0 defeat of West Ham United in their previous fixture guaranteed Premier League survival for the Eagles.
Manager Tony Pulis has guided Palace to 12 wins in 26 matches since taking over from Ian Holloway in November, but the Eagles never looked like adding to that tally against Pellegrini's title challengers.