Phil Foden earned Manchester City a late 1-0 win at Goodison Park just when it looked like Everton would give Merseyside rivals Liverpool a hand in the title race.
Everton had frustrated the leaders for 82 minutes with a brilliant defensive performance led by Jordan Pickford.
The Everton goalkeeper denied Foden and Joao Cancelo in quick succession before a fantastic double save from Kevin De Bruyne's low shot and Bernardo Silva's follow-up.
But with the match heading towards a stalemate, Foden took advantage of Michael Keane's slip to score from close range.
Richarlison had a chance to equalise but could not beat Ederson as City extended their lead to six points ahead of next weekend's Manchester derby. Second-placed Liverpool have a match in hand.
A fifth defeat in seven leaves Everton a point and a place above the relegation zone.
Everton: 7 Mar v Spurs (A)
Man City: 6 Mar v Man Utd (H)
Referee: Paul Tierney. Assistants: Lee Betts, Stuart Burt. Fourth official: Martin Atkinson. VAR: Chris Kavanagh. Assistant VAR: Gary Beswick.