City’s Kevin De Bruyne netted twice and top-scorer Erling Haaland hit his 19th league goal of the season, with Rico Lewis also on the scoresheet.
The win lifts City to 70 points — behind leaders Liverpool on goal difference — ahead of Arsenal’s match at Brighton later on Saturday, where a win for the Gunners would send them top.
Jurgen Klopp’s Liverpool face a trip to mercurial Manchester United at Old Trafford on Sunday in the next chapter of a thrilling three-way title race.
Jean-Philippe Mateta gave Crystal Palace a shock early lead at Selhurst Park in the early kick-off but De Bruyne levelled in the 13th minute with a curler into the top corner to quell any nerves from the visitors.
Palace carried an attacking threat but Lewis put City ahead just after half-time and De Bruyne and Haaland combined for the third.
Midfielder De Bruyne added his second with a solo effort in the 70th minute — his 100th goal for the club — to make the game safe, before substitute Odsonne Edouard scored a consolation.
City boss Pep Guardiola hailed the Belgium international, who missed five months of the season with a hamstring injury he sustained in the opening match at Burnley.
“Sometimes it’s Phil (Foden), Erling or Julian (Alvarez), today it was Kevin,” he said.
“Without him we would not be able to win this. You talk about managers but players like Kevin make this game easy.”
Everton end miserable run
Everton went into their match against second-from-bottom Burnley desperately searching for a spark of inspiration after a run of 13 Premier League matches without a win.
They struggled to impose themselves but benefited from a huge error from visiting goalkeeper Arijanet Muric in first-half stoppage time.
Muric took too much time to clear the ball and when he did it was straight at Dominic Calvert-Lewin, with the ball rebounding off the forward into the net.
The win means Everton are now four points above the relegation zone.
But the club need everything they can get as they wait nervously to find out if they will be handed a second points deduction this season for breaking Premier League financial rules.
Fourth-placed Villa, beaten in midweek by City, will rue a second-half collapse that could prove costly in their chase to qualify for next season’s Champions League.
Unai Emery’s men drew 3-3 against Brentford but only after tossing away a 2-0 lead.
Villa led 2-0 moments into the second half after goals from Ollie Watkins and Morgan Rodgers but three goals in nine minutes from Mathias Jorgensen, Bryan Mbeumo and Yoane Wissa turned the match on its head.
Watkins scored his second goal of the game in the 80th minute but Villa could not find a winner and they are just three points above fifth-placed Tottenham, who have two games in hand.
Carlton Morris scored a 90th-minute goal in Luton’s 2-1 win against Bournemouth — a result that leaves them in the relegation zone but now level on points with 17th-placed Nottingham Forest.
Newcastle beat Fulham 1-0 courtesy of a late goal from Bruno Guimaraes to keep alive their hopes of European football next season while West Ham came from behind to beat Wolves 2-1.
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