Phil Foden secured arguably the biggest three points of his career as Man City kept their title hopes in their own hands ahead of the fast-approaching Liverpool.
Emotional pre-match displays of support for Ukrainians Oleksandr Zinchenko and Vitaliy Mykolenko left the players in tears, but Everton shook off the to put in a solid display.
Man City still came away winners, but they didn't do it entirely of their own volition, with an 'unbelievable bit of bad luck' putting Everton behind with eight minutes to play.
Frank Lampard's men were then denied their shot at a dramatic late equaliser when City's Rodri controlled the ball in his box with his upper arm.
Premier League rules state the sleeve part of a player's arm doesn't count for a handball, but former Man City player and talkSPORT commentator Trevor Sinclair was shocked to see VAR not award a spot-kick.
"This is why the VAR has not been interpreted right and the big clubs get the big decisions," the Man City fan said.
"I think it's more arm than it is shirt.
"I think that's Manchester City being a big club and getting the decision in their favour."
The penalty wasn't City's only bit of luck either, with a botched Keane interception falling to Foden who brilliantly danced round Jordan Pickford to poke home the winner.
Everton had put in a resilient display to keep the game scoreless for 81 minutes, but were unable to deal with a Bernardo Silva cross.
Keane's interception was a the first huge slice of luck for City according to Sinclair.
"That's an unbelievable bit of bad luck there for Everton, they've defended so well," the former striker said.
"It's really fortunate. They've not made that goal, it's fortunate."