Match ends, Manchester City 3, Everton 1.
Gabriel Jesus said his mother's arrival in England has improved his confidence as he ended his Premier League goal drought to help Manchester City return to the top of the table.
Jesus had not scored a league goal since August - a run of 11 games and 487 minutes - but netted twice before Raheem Sterling added City's third.
The Brazil forward, who signed for City in 2017 and extended his contract until 2023 earlier this season, has recently been joined in Manchester by his mother.
"My confidence is back because my family is here with me," said the 21-year-old.
"They help me a lot. It is easy for me because they are everything. I need my family in this moment."
City manager Pep Guardiola said: "He settled so well from the beginning - but it is much better his family is here and strikers need to score goals.
"He scored two nice goals that will be important for him."
City will stay top 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.
This victory, City's 10th in a row at home in the league, 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.
Jesus 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 - a week after suffering alleged racial abuse during City's defeat at Chelsea - heading in Fernandinho's cross four minutes later with his first touch.
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.
De Bruyne back and Aguero on the bench
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.
"The players responded [to defeat at Chelsea] in a marvellous way," Guardiola said.
"Everton have top players. Today was tricky - a dangerous, dangerous game.
"They drew at Stamford Bridge, at Liverpool it came down to the last second. I am very pleased."
Everton show plenty of attacking ambition
Everton have now gone four games without a win but with better finishing they could at the very least have made the scoreline closer on Saturday.
Richarlison, so often their hero this season, was first to blame when he blasted wastefully over after arriving in space to meet Digne's cross at the back post.
That was the Toffees only effort at goal in the first half, but they were much more lively once they had fallen 2-0 down after the break.
The Toffees have chiefly relied on Richardson and Gylfi Sigurdsson for their goal threat this term, but Calvert-Lewin was a handful throughout.
He has only scored twice since the start of September but could have had two in 45 minutes here, if not for a fine Ederson save to keep out his clever flick.
Everton manager Marco Silva bemoaned the missed chances after the match.
"Until the moment they scored the game was what we expected," said the Portuguese.
"We were blocking them and they didn't create one chance before they scored the first goal.
"The biggest chance was our chance with Richarlison. Against this team we have to be effective when we create moments to score.
"We made a mistake with the first goal, they scored and after that they were more comfortable."
Man of the match - Leroy Sane (Man City)
City's fine home run - the best stats
- Manchester City have won all 21 of their games this season when they have scored in the first half. The only five games they have not won this term are the five in which they have not scored in the first half.
- City have won their past 10 Premier League home games, scoring 36 and conceding seven goals.
- Everton have won only one of their past nine away league matches, losing five.
- Since Guardiola became City manager, Everton have scored more Premier League goals against them - eight - than any other team.
- Sane set up both of Jesus' goals on Saturday, his first two assists in the league for the Brazilian.
- City forward Sterling scored only his second headed goal in the Premier League, and his first since one against Sunderland in December 2015.
- Since the start of last season, no Everton player has scored more goals than Calvert-Lewin (13, level with Sigurdsson).
City continue their defence of the Carabao Cup at Leicester on Tuesday (19:45) and return to the Etihad next Saturday to host Crystal Palace in their final league game before Christmas (15:00).
Everton host Tottenham in their next Premier League game on Sunday, 23 December (16:00).
- 18DelphBooked at 76mins
- 20Bernardo Silva
- 26MahrezSubstituted forDe Bruyneat 75'minutes
- 33Gabriel Jesus
- 19SanéSubstituted forSterlingat 66'minutes
- 17De Bruyne
- 23ColemanSubstituted forWalcottat 57'minutes
- 12DigneBooked at 19mins
- 8André Gomes
- 10G SigurdssonSubstituted forDaviesat 81'minutes
- 20BernardSubstituted forLookmanat 57'minutes
- 29Calvert-LewinBooked at 76mins
- Craig Pawson
- Shots on Target
Second Half ends, Manchester City 3, Everton 1.
Foul by Fernandinho (Manchester City).
Ademola Lookman (Everton) wins a free kick in the attacking half.
Foul by Bernardo Silva (Manchester City).
Ademola Lookman (Everton) wins a free kick in the defensive half.
Corner, Everton. Conceded by Kyle Walker.
Foul by Kevin De Bruyne (Manchester City).
Theo Walcott (Everton) wins a free kick on the right wing.
Attempt missed. Dominic Calvert-Lewin (Everton) header from the right side of the six yard box misses to the left. Assisted by Lucas Digne with a cross following a corner.
Corner, Everton. Conceded by Nicolás Otamendi.
Attempt blocked. Richarlison (Everton) right footed shot from outside the box is blocked. Assisted by Ademola Lookman.
Attempt saved. Dominic Calvert-Lewin (Everton) right footed shot from the centre of the box is saved in the bottom left corner. Assisted by Theo Walcott with a cross.
Substitution, Everton. Tom Davies replaces Gylfi Sigurdsson.
Attempt missed. Ademola Lookman (Everton) right footed shot from outside the box is high and wide to the right. Assisted by Dominic Calvert-Lewin.
Offside, Everton. Yerry Mina tries a through ball, but Dominic Calvert-Lewin is caught offside.
Dominic Calvert-Lewin (Everton) is shown the yellow card.
Fabian Delph (Manchester City) is shown the yellow card.
Ilkay Gündogan (Manchester City) wins a free kick in the defensive half.
Foul by André Gomes (Everton).