Tim Cahill suffered mixed emotions as he scored Everton's winner but was then sent off by referee Steve Bennett for an over-exuberant celebration.
Everton's £2m summer signing from Millwall headed home on the hour to seal a richly-deserved victory.
David James, dropped by England for the World Cup qualifier in Poland, kept Everton at bay with saves from Steve Watson, Marcus Bent and Leon Osman.
City barely troubled 10-man Everton in a bitterly disappointing display.
James was the central figure in a first 45 minutes that saw City enjoy the greater share of possession but Everton carve out the clearer chances.
He was in action after 11 minutes, making a fine double save from Steve Watson after he had been played in by Leon Osman.
James then denied Marcus Bent when he somehow kept out his header at point-blank range as he stole in on Lee Carsley's free-kick.
Leon Osman was next to be frustrated from only 10 yards, but the youngster should have scored after being set up by Cahill.
City only created half chances, and the game was enlivened in first-half injury time when Carsley and Joey Barton were both booked after a crunching challenge.
Everton deservedly took the lead on the hour - but it was a bitter-sweet moment for Cahill.
The Australian timed his run perfectly to head Tony Hibbert's cross past James.
But as he celebrated his goal, referee Bennett stunned players and supporters alike by sending Cahill off for over-exuberance.
Everton held out in relative comfort in the closing stages, with only Sylvain Distin causing alarm, firing narrowly over from the edge of the area.
Man City: James, Mills, Dunne, Distin, Thatcher (Jihai 73), Wright-Phillips, Reyna, Barton, Sinclair (Sibierski 73), Anelka, Fowler (Macken 63). Subs Not Used: Waterreus, Bosvelt.
Everton: Martyn, Hibbert, Weir, Stubbs, Pistone,
Osman (Gravesen 58), Watson, Carsley, Cahill,
Kilbane (Naysmith 73), Bent (Ferguson 73).
Subs Not Used: Wright, McFadden.
Sending Off: Cahill (61).
Booked: Carsley, Cahill, Pistone.
Goals: Cahill 60.
Ref: S Bennett (Kent).