Riyad Mahrez scored the pick of the goals in between Phil Foden and Bernardo Silva’s strikes as Pep Guardiola’s men took another huge step towards a third title in four years.
Richarlison’s first-half equaliser was little consolation for seventh-placed Everton, who have now won just one of their last six league games to fall five points behind in the battle for a top-four finish.
This fixture was rearranged from late December due to a coronavirus outbreak affecting multiple players at City that threatened to derail their title challenge.
Guardiola’s side were eighth in the table at the time, but have not dropped a point in their 10 league games since to streak clear of the chasing pack.
The visitors were without the in-form Ilkay Gundogan due to a groin injury picked up in Saturday’s 3-0 win over Tottenham, while Kevin De Bruyne was fit to return from a hamstring problem but only from the bench.
Sergio Aguero was also among the substitutes, but Gabriel Jesus has failed to make the most of his chance to shine in the absence of the Argentine for most of the season and the Brazilian had another off night in front of goal.
Jesus blazed over City’s best chance as the hemmed Everton into their own half.
When the deadlock was broken there was a hint of fortune to it as Foden’s shot deflected off Seamus Coleman to leave the helpless Jordan Pickford wrong-footed.
Carlo Ancelotti’s men had shown no attacking intent until conceding, but were immediately rewarded for pushing forward after falling behind as Lucas Digne’s shot came back off the post and ricocheted in off Richarlison.
That was just the second goal City have conceded in nine league games, but there still seemed little doubt they would find a way to extend their winning run.
Pickford saved well from Silva at his near post and Jesus fired another inviting opening over from a narrow angle before a moment of the highest quality saw City restore their lead.
Silva’s cushioned pass teed up Mahrez on the edge of the box and his sumptuous curling effort clipped the inside of the far post on its way into the net.
The roles were reversed for the visitors’ third 13 minutes from time as Mahrez and Jesus picked out Silva on the edge of the box and his shot had too much power for Pickford.
Guardiola could then afford the luxury of giving De Bruyne the final 15 minutes after a month on the sidelines to try and get the Belgian up to full match fitness before City return to Champions League action in the last 16 at Borussia Monchengladbach next Wednesday.