The Brazilian netted either side of half time to put the champions in control of the contest, but Everton threatened to set up a nervy finale when Dominic Calvert-Lewin pulled a goal back shortly after the hour mark.
However, Raheem Sterling quickly restored City's two-goal lead as they maintained their 100% home record in the league this season, moving above Liverpool into first place at least until the Reds face Manchester United on Sunday.
City named the likes of Sergio Aguero, Sterling and Kevin De Bruyne on a star-studded bench as they went in search of a response to their first league defeat of the season last weekend, and they quickly took control of the possession at the Etihad.
It was not until the 15th minute that either side registered a shot, though, and it came from Everton as an unmarked Richarlison blasted his volley over the crossbar when he should have done better from Lucas Digne's delivery.
City responded with their first effort seconds later when Jordan Pickford collected Fabian Delph's long-range shot, and the makeshift full-back blasted another powerful strike narrowly over the crossbar after 20 minutes as the hosts began to increase their pressure.
The opening goal almost came from the foot of an Everton player when Michael Keane got his toe to a cross ahead of Jesus, forcing Pickford to make a brilliant reaction stop to deny the Toffees a second own goal in the Premier League this week.
It was only a temporary reprieve, though, as City broke the deadlock just a minute later. Yerry Mina gave the ball away while trying to play out from the back and was ruthlessly punished, with Leroy Sane providing the killer pass for Jesus to sweep his finish past Pickford.
A second almost followed on the half-hour mark when Aymeric Laporte got the wrong side of Keane, but the Everton defender did just enough to disrupt his headed finish from inside the area.
The hosts continued to control proceedings and should have doubled their advantage five minutes before the interval when a deflected cross fell kindly for Riyad Mahrez inside the area, only for the winger to put his finish too close to Pickford.
The second goal did arrive five minutes after the break, though, and it was the same duo who combined for the first as Sane clipped a cross into the box for Jesus, who powered a bullet header past Pickford to double his personal tally.
At that stage it looked as though City were in complete control of the contest, and they almost put the game to bed once and for all when Ilkay Gundogan played a one-two on his way into the box before firing wide of the near post.
However, Everton gave themselves a glimmer of hope shortly after the hour mark when they pulled a goal back through Calvert-Lewin, who rose to meet Digne's cross with a firm header which took a nick off Delph on its way into the bottom corner.
Pep Guardiola responded to that by bringing Sterling on, and the in-form winger made an immediate impact by restoring City's two-goal advantage with a close-range header of his own after good work from Fernandinho down the left channel.
Everton will be left feeling as though they had the chances to cause an upset, though, and Richarlison squandered another of those moments after City's third when he blazed over from the edge of the box.
Ademola Lookman produced a positive cameo appearance off the bench for the visitors and almost created a second for Everton when his low cross was turned over from close range by fellow substitute Theo Walcott.
City were able to hand a long-awaited return to De Bruyne in the final 15 minutes, but it was Everton who looked most like adding to the scoring in the closing stages, with Lookman and Richarlison both firing off target from range and Calvert-Lewin seeing an audacious mid-air flick comfortably gathered by Ederson.
The hosts saw the match out relatively comfortably, though, and have now won all nine of their Premier League home games this season, whereas Everton remain seventh and have now won just one of their last six outings.
MAN CITY (4-3-3): Ederson; Walker, Otamendi, Laporte, Delph; Bernardo, Fernandinho, Gundogan; Mahrez (De Bruyne 75'), Jesus, Sane (Sterling 66')
EVERTON (3-4-3): Pickford; Keane, Zouma, Mina; Coleman (Walcott 57'), Sigurdsson (Davies 81'), Gomes, Digne; Bernard (Lookman 57'), Calvert-Lewin, Richarlison