Erling Haaland, sporting a black armband in honour of the late Norwegian King Harald V - whose death was announced earlier on Friday - nodded in the 17th-minute opener as well as an 84th-minute cushion.
Enzo Maresca made just one change from their season-opening win over Bournemouth, with Cherki replacing Rico Lewis.
It proved prescient in a wild six-minute spell in the second half initiated by Cherki's first goal, in the 54th minute, before Gianluigi Donnarumma's own goal from Yeremy Pino's free-kick.
Palace barely had a chance to celebrate before Cherki found the bottom corner three minutes later, and Haaland added a late second to make it two Premier League wins from two matches for the new City boss.
With England boss Thomas Tuchel watching on from the stands, Adam Wharton fed the ball to Eddie Nketiah, who was trapped on the wrong side of Ruben Dias and could only fire into the side-netting.
There was a blocked Daichi Kamada effort and a pair of Palace corners before City took control and Elliot Anderson forced Dean Henderson into a diving save.
The ball fell loose and Jorgen Strand Larsen, also sporting a black armband, thwarted compatriot Haaland's attempt at close-range finish with an alert clearance from the ensuing scramble.
The Norwegian would not be denied a second time and nodded City in front with a looping header from Antoine Semenyo's cross.
There was a chance for the unmarked Tyrick Mitchell to draw the sides level before the break from Wharton's cross, but the chance was squandered when he nodded the ball wide.
Nketiah stabbed wide as the second half started before Cherki doubled City's advantage, taking advantage of some poor organisation from home defence and neat footwork to slot the ball beyond Henderson's outstretched foot.
The hosts halved the deficit two minutes later from Pino's excellent free-kick, which rattled off a post and hit Donnarumma on the back before finding the net.
City responded three minutes later and it was Cherki again, whose strike appeared to take a small deflection off Chris Richards and past Henderson to restore their two-goal lead.
The hosts were briefly left short-handed after referee Andrew Madley enacted the new 10-second substitution rule as Oscar Mingueza's Premier League debut was momentarily delayed, but they were back at full strength when Haaland lifted the ball beyond Henderson with six minutes remaining.
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