Pep Guardiola’s side will stay for at least another day, with Liverpool needing to beat Manchester United at Anfield on Sunday (16:00 GMT kick-off) to reclaim their place at the summit.
Raheem Sterling came off the bench to add the hosts’ third with his first touch, a week after suffering alleged racial abuse during City’s defeat at Chelsea.
This victory, City’s 10th league win in a row at home, was rarely in serious doubt once Jesus had fired his side ahead on a bitterly cold day at Etihad Stadium.
Yerry Mina’s misplaced pass allowed Ilkay Gundogan to find Leroy Sane in space, and he sent Jesus galloping into the area to score with a fine low finish.
It was the Brazilian’s first league goal since August – a run of 11 games and 487 minutes without finding the net – but he only had to wait another 28 minutes for his second of the game.
When it arrived just after half-time, Sane was the provider again – with Jesus meeting his precise cross to plant an unstoppable header past Toffees keeper Jordan Pickford.
City looked in complete control but Everton gave themselves hope just after the hour when Dominic Calvert Lewin met Lucas Digne’s cross to reduce the deficit.
The visitors were only briefly back in it, however, with substitute Sterling heading in Fernandinho’s cross four minutes later.
It was enough to ensure City, whose loss at Stamford Bridge last weekend was their first in the league this season, are back in a familiar position at the top.
Kevin de Bruyne, back from a knee injury that has kept him out of action since 1 November, also came off the bench before the end to give the home fans further reason to cheer.
The hard work was done by the time De Bruyne emerged from the relative warmth of the bench with 16 minutes remaining, but the welcome he received from the home fans showed how pleased they were to see him back.
Before Saturday’s game, the Belgium midfielder had played only 236 minutes out of a possible 2,250 in 2018-19 because of injuries to both of his knees.
This was only his sixth appearance of the season, with Guardiola hoping that will mean the27-year-old will be “fresh” for the busy festive period.
De Bruyne’s return was not the only good news for Guardiola, with striker Sergio Aguero fit enough to be among the substitutes after missing the past four games with a groin problem.
In the end, the Argentine was not needed but, like De Bruyne, he will surely have a big part to play in the weeks ahead.
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