Erling Haaland and Rayan Cherki both scored two as Enzo Maresca’s men turned on the style at Selhurst Park.
Haaland headed City in front in the first half with a looping header from an impressive Antoine Semenyo cross.
The Blues could – and probably should – have been more ahead at the break but the visitors more than made up for it with a stylish second half showing.
Cherki doubled the lead with a lovely finish following an incisive run into the box.
Palace pulled one back with a Yeremy Pino free-kick piledriver which went down as a Gianluigi Donnarumma own-goal.
But Cherki restored our two-goal advantage with a superb strike before Haaland added another just before the end to clock up six points from our opening two games.
Watch brief highlights in the video player above.