Jesus had not scored in the league since August but, with Sergio Aguero among the substitutes after recovering from a groin injury, the Brazil international led the line superbly as Pep Guardiola's side returned to the summit.
Everton's Dominic Calvert-Lewin scored to cut a two-goal deficit in half but substitute Raheem Sterling, who was allegedly the subject of racial abuse from supporters at Stamford Bridge a week ago, scored the game's crucial fourth goal.
Richarlison missed a fine opportunity to put Everton ahead when he arrived unmarked at the far post but volleyed Bernard's cross high and wide, failing to apply the spectacular finish he intended.
The Toffees were shaping up to give City a tough game only to concede a sloppy opener, Yerry Mina's clearance leading to Leroy Sane playing in Jesus, who guided the ball under the body of the advancing Jordan Pickford.
Pickford made a superb save from Riyad Mahrez at close range before the break but could do little with City's second goal five minutes into the second half, Jesus meeting Sane's curling ball with a clinical header that flashed beyond the England goalkeeper.
There was a mix-up in the City defence when Lucas Digne's looping cross was headed down into the net by Calvert-Lewin via a deflection off Fabian Delph, but Sterling quickly dismissed any ideas of a comeback.
Less than four minutes after replacing the disgruntled Sane, the forward ghosted into the six-yard box to head home Fernandinho's cross from City's left flank.
What does it mean? Over to you, Liverpool
Liverpool entertain Manchester United at Anfield and while Jose Mourinho's men have struggled this season to make an impression at the top end of the table, City's result in Saturday's early kick-off heaps the pressure on Jurgen Klopp's side to keep pace in the title race.
Jesus resurrects form of last season
After finding the net 13 times in the league for the champions in 2017-18, Jesus has found goals tougher to come by so far this term. Guardiola will hope the striker's well-taken double, coupled with an impressive all-round performance, can lead to a productive spell during a busy run of fixtures.
Mina mishap costs Marco Silva's men
Everton - who had drawn each of their last three away games against City in the Premier League - had made an impressive start before Mina's careless clearance set the wheels in motion for the opening goal, with the Colombian defender needlessly giving up possession to Ilkay Gundogan.
Key Opta Facts
- City have won their last 10 Premier League home games, scoring 36 and conceding just seven.
- Everton have won just one of their last nine Premier League away games (D3 L5).
- Since Pep Guardiola took charge, Everton have scored more Premier League goals against City than any other side (8).
- Gabriel Jesus' opener was his first Premier League goal since August, ending a barren spell spanning 487 minutes that included 18 shots.
- Leroy Sane assisted both of Jesus' goals in this game - the German had never previously assisted the Brazilian in the Premier League.
- Raheem Sterling scored just his second headed goal in the Premier League, the other coming in December 2015 against Sunderland.