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Cherki and Erling Haaland both opened their accounts for the new campaign with two goals apiece. Haaland opened the scoring with a first-half header, but Cherki's dazzling brace stole the show.
Cherki's first goal highlighted his blistering speed as he weaved through Palace defenders before beating Dean Henderson with a clever left-footed finish.
Palace briefly narrowed the deficit, but Cherki struck again almost immediately to end hopes of a comeback. Haaland then added a late fourth to complete City's second straight league victory.
Despite his match-winning contribution, Cherki was self-critical, admitting he felt he had played poorly in the first half and needed to share the ball more.
New Manchester City manager Enzo Maresca will have been pleased with the performance, while Haaland remained confident about the team's early-season progress.
Haaland pointed to the team's shortened pre-season and Cherki's recent World Cup campaign, expressing confidence that City will improve with each match under their new coach.