The Sky Blues faithful were stunned into silence by Jean-Philippe Mateta's early strike, and City were guilty of some sloppy play in the early exchanges, but Kevin De Bruyne's stunning strike sent the visitors into half time on level terms.
The promising start Oliver Glasner's side made soon petered out, though, as Rico Lewis and Erling Haaland put City out of sight before De Bruyne hit his century for the Citizens, ensuring that Odsonne Edouard's late goal would be a scant consolation.
With Real Madrid on the horizon, Pep Guardiola threw a selection surprise by introducing Oscar Bobb into the first XI over Phil Foden, while Palace jewel Michael Olise made the bench for the hosts.
Not since pre-COVID times in 2019 had Crystal Palace made the net bulge in a Premier League home match with Man City, who were expected to take a firm grip on proceedings from the off, but Guardiola threw his arms up in despair with just three minutes gone.
One defence-splitting pass from Adam Wharton set Mateta away, as the Frenchman burned John Stones for pace and let fly with a low strike across the box, which hit the inside of the post before trickling over the line.
The customary City possession dominance followed Mateta's shock opener, but Dean Henderson stood tall in the Palace goal, thwarting Julian Alvarez and Rodri with two top saves in the space of two minutes.
However, the ex-Manchester United stopper was helpless to prevent the champions quickly drawing level in the 13th minute, as De Bruyne picked the ball up in the right-hand side of the box, cut inside Wharton and fired an unstoppable curler into the top corner.
Chances continued to arrive at both ends during a frenetic start, as Jordan Ayew's volley in the 18th minute was not a million miles over the top, one moment before Henderson came up trumps in a one-on-one with Haaland after De Bruyne's incisive through ball.
The contest unsurprisingly slowed down a notch in the second half of the opening period, although an uncharacteristic mistake from Rodri in the 37th minute presented Ayew with a promising opening, which he failed to take as he struck the top of the bar.
City's Spanish midfield maestro was not enjoying his finest hour at Selhurst Park and also put his goalkeeper in a hole in the 43rd minute, playing the ball back to Stefan Ortega unaware of Mateta's presence, but the champions' number two phenomenally escaped the danger with an exquisite touch to take the chance away from the Frenchman.
With City's left flank found wanting in the opening period, Guardiola saw fit to swap Josko Gvardiol out for Manuel Akanji at half time, and the champions finally breached Henderson's goal for a second time just two minutes into the second period.
Coincidentally, it was an attack down the left which did the damage, as Joachim Andersen nodded a Jack Grealish delivery into the path of Lewis, whose effort took a nick off of Jefferson Lerma's boot and nestled into the bottom corner.
Guardiola's charges should have been out of sight in the 54th minute, but Alvarez's fierce low effort was blocked en route to goal by a floored Andersen, down on the ground holding his face following an earlier altercation with Haaland.
However, City would eventually bag the insurance goal in the 66th minute via another well-worked move down the left, which saw Grealish and De Bruyne combine before the latter's toe-poke from the byline was met by Haaland for a simple finish.
With their tails up, the visitors carved through the Palace backline like butter again in the 70th minute, as Rodri's cute touch teed the ball up for De Bruyne, whose swerving low strike flew in at Henderson's near post for his 100th Man City goal in all competitions.
Following the Belgian's landmark strike, Palace were simply waiting for the full-time whistle in front of a subdued atmosphere, although Ruben Dias and Stones both had to deflect an Edouard effort to safety after the Eagles won the ball back high up the field.
The former Celtic man would reduce the deficit in the 86th minute, though, getting across Dias to meet Tyrick Mitchell's cross and delicately toe-poking the ball past Ortega, but more late pressure from the hosts would amount to nothing.
Saturday's success temporarily lifts Man City into second place above Arsenal, who can regain the silver medal position against Brighton & Hove Albion this evening, while Glasner's men remain 14th, eight points clear of the drop zone.
The small matter of Tuesday's Champions League quarter-final first leg with Real Madrid is next on the agenda for Man City, while Palace have a full week to recover before another tough examination against Liverpool at Anfield next Sunday.