The win sent City to the top of the table following their opening 2-1 win over Bournemouth, while Palace lie dead last after back-to-back defeats.
Palace nearly made a dream start to the contest, but Gianluigi Donnarumma denied Eddie Nketiah inside two minutes. City soon responded, with Dean Henderson saving Elliot Anderson's long-range effort before Erling Haaland's rebound was blocked.
Haaland eventually broke the deadlock in the 17th minute, directing Antoine Semenyo's delivery into the top corner for his first goal of the new campaign. City had chances to extend their lead before half-time, with Phil Foden twice missing from promising positions, while Tyrick Mitchell headed wide for Palace.
City doubled their advantage in the 54th minute when Foden found Cherki, who weaved past challenges before calmly beating Henderson. Palace pulled one back soon after when Yéremy Pino's long-range free-kick struck the post and rebounded in off Donnarumma.
Cherki restored City's two-goal lead before the hour with a powerful strike that took a deflection off Chris Richards and flew into the top corner. City then controlled the remainder of the match, with Haaland adding a fourth late on from another Foden assist.
"It is a tough ground," new Man City boss Enzo Maresca said after the game. "We knew it before the game. You saw it in the first few minutes of the game. But then we were in control. The intensity, the desire of the team has been very good."
Maresco also had special praise for Rayan Cherki, who was named player of the match after his two-goal haul.
"He's helping us. He's going to help us in the future. We know he's a quality player, last game against Bournemouth with two assists, today with two goals. But I think Rayan was very good off the ball. He was in control of Wharton and he worked very hard."
