Phil Foden scored his first top-flight goal of the season in stoppage time to pull one back but it proved to be too little too late for the flailing champions, whose spark has vanished.
City have now lost six Premier League games in the current campaign, twice as many as they suffered during the whole of last season, when they were crowned champions for a fourth straight season.
They are realistically out of the title race already - nine points behind leaders Liverpool having played two games more, while Villa leapfrogged them into fifth spot.
Palace will be sick of the sight of former Manchester City forward Jesus, who scored a hat-trick against them in the League Cup quarter-finals at the Emirates on Thursday (NZT).
Jesus netted twice in the first half and was only denied a third by the width of a post, with Kai Havertz reacting quickly to convert.
Palace forward Ismaila Sarr, who had pulled his team level at 1-1, failed to make the most of two inviting opportunities early in the second half.
Instead, Arsenal added two more, climbing back above Nottingham Forest, who leapfrogged them earlier in the day.
But Mikel Arteta - celebrating five years in charge at Arsenal - will be concerned after Bukayo Saka limped off midway through the first half.
Jesus opened the scoring in the sixth minute, finishing confidently after fine work from Saka on the right wing for his first Premier League goal since January.
But Palace were level just five minutes later when Sarr collected a Tyrick Mitchell pass, opening his body and bending the ball past the diving David Raya.
Arsenal’s second came after a corner, with Jesus steering the ball in off the post with pinpoint precision when it fell to him.
Brimming with confidence, he headed against a post in the 38th minute, with Havertz following up to tap in.
Sarr could have done better with a diving header from close range in the opening minutes of the second half but Raya got down low to save.
Raya was called into action again minutes later, keeping out Jean-Philippe Mateta’s fierce drive from distance and clutching the ball from Sarr’s header on the follow-up.
Gabriel Martinelli of Arsenal celebrates against Crystal Palace. Photo / AFP
But Palace were unable to reduce the deficit and instead Arsenal stretched their lead -- again Jesus could have completed his hat-trick.
Palace goalkeeper Dean Henderson denied the Brazil international but substitute Declan Rice made good contact with the ball and Gabriel Martinelli turned it in from close range.
Rice scored himself in the 84th minute to make it five, curling a shot from the edge of the box into the far corner.
Arteta spoke on Friday about how the “best was yet to come” as he celebrated his five-year anniversary at the Emirates, saying he was aiming for the “big trophies”.
The Gunners, who have not won the Premier League since 2004, are now just three points behind leaders Liverpool but Arne Slot’s team have played two games fewer.
Forest won their third consecutive Premier League match to keep up their push for European football, condemning Brentford to their first home defeat this season.
Coming into the game, Thomas Frank’s team boasted the best home record in the league, with seven wins and a draw from their eight games at the Gtech Community Stadium.
But they came unstuck against Nuno Espirito Santo’s in-form team.
Ola Aina slotted home the opener towards the end of the first half and Anthony Elanga made it 2-0 early in the second period.
Newcastle deepened Ipswich’s plight and lifted themselves to seventh in the table with a 4-0 win at Portman Road.
Isak volleyed Eddie Howe’s team ahead in the first minute and Jacob Murphy doubled their lead before Isak side-footed in from close range just before the break.
The Sweden international scored his third nine minutes into the second half, poking the ball home after more fine work from Murphy.
It was a ninth defeat in 17 games for Ipswich since they returned to the Premier League and they remain in the relegation zone, two points from safety.
Mats Wieffer gave Brighton a 51st-minute lead against West Ham but Mohammed Kudus equalised seven minutes later and the match finished 1-1.
Premier League leaders Liverpool face a tricky trip to Tottenham on Monday while second-placed Chelsea visit Everton among five matches.