Goals from Romelu Lukaku, Kevin Mirallas, Tom Davies and Ademola Lookman gave the Toffees all three points and handed Pep Guardiola his worst ever league defeat in management.
The result leaves City 10 points behind league leaders Chelsea.
Lukaku opened the scoring in the 34th minute after slotting home a low cross from Mirallas to beat Bravo.
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The home side controlled proceedings after Lukaku’s opener and doubled their advantage one minute into the second half after Mirallas low shot from the edge of the area found the back of the net.
Davies made it three in the 79th minute with a beautiful chip over Bravo, with Lookman who made his Premier League derby adding the icing to the cake with a powerful drive through Bravo’s leg.
“To actually go out there and do it, it’s unbelievable. It hasn’t quite sunk in yet. It’s surreal, being with the first team in general but today to beat City and do it comfortably, it’s a great day,” Davies daid on scoring his first goal for Everton.
Next up for City is a home game against Tottenham Hostpur on Saturday.