Danny Mills' stunning 25-yard strike set Manchester City on the road to victory and kept Everton rooted to the bottom of the Premiership table.
Mills sparked a wretched game into life after 71 minutes with a long-range drive that flew high past Nigel Martyn.
Darius Vassell wrapped up a deserved win for City with a goal in the dying seconds from Joey Barton's pass.
Sylvain Distin cleared off the line from David Weir late on, while City's Antoine Sibierski was denied by Martyn.
It put Stuart Pearce's side back on track after successive Premiership defeats - but his Everton counterpart David Moyes is contemplating a crisis after going out of Europe and with only one league goal this term.
City's Barton recovered from an ankle injury, while Andy Cole was fit again and able to return after a hamstring problem.
Everton were without Mikel Arteta after he suffered a neck injury in the Uefa Cup clash against Dinamo Bucharest on Thursday.
The early kick-off was no excuse for a dismal first 45 minutes that was devoid of any attacking ideas or quality.
Everton's Leon Osman had a header off target from Matteo Ferrari's cross, while Tim Cahill's header was ruled out for a clear offside.
City also struggled to make any impact, with little of their early-season momentum in evidence.
Barton livened up the crowd after 58 minutes, with a crunching tackle on former Manchester United star Phil Neville that earned a yellow card - and arguably the biggest cheer of the match so far.
Kiki Musampa had a half-chance three minutes later but he could only hit the side-netting.
It was his last contribution as he was replaced by Lee Croft, with Everton also sending on James Beattie for Marcus Bent.
City finally made the breakthrough with 19 minutes left, courtesy of a moment of quality completely out of keeping with the rest of the game.
Mills advanced on the right-flank, then cut in and lashed an unstoppable 25-yard shot past Martyn.
Sibierski almost doubled City's lead with seven minutes left when he got on the end of Croft's cross but Martyn made a crucial block.
And as Everton pressed forward in the dying seconds, Barton played in Vassell with a precise pass to beat Martyn and wrap up the points.
Manchester City boss Stuart Pearce:
"There were not a great deal of chances in the game and then Danny Mills comes along and scores a wonder goal - and it was a wonder goal, make no mistake.
"It was absolutely unstoppable. Pele would have been proud of a strike like that. It was an absolutely incredible strike.
"I was a bit disappointed that we didn't play with as much tempo as I would like and we didn't pass the ball as well as we would like but it is a good result for us and we will take it.
"We can now go away and work on things we can improve and hope to do them better next time."
Everton manager David Moyes:
"We are obviously short at the moment. We can't score any goals.
"We got one against Dinamo Bucharest in midweek and our performance was much better then. It gave us confidence coming into this game, but we didn't create enough going forward.
"It is the responsibility of the whole team, not just one individual or the attackers.
"We knew we weren't playing as well as we should be, but we were still in the game until a wonder goal from Danny Mills changed it. "
Man City: James, Mills, Dunne, Distin, Jordan, Musampa (Croft 63), Barton, Sibierski, Ireland, Cole (Jihai 90), Vassell.
Subs Not Used: Sommeil, Onuoha, De Vlieger.
Goals: Mills 72, Vassell 90.
Everton: Martyn, Ferrari, Yobo, Weir, Nuno Valente, Osman (Davies 75), Cahill, Neville, Kilbane, Bent (Beattie 63), McFadden (Ferguson 70).
Subs Not Used: Wright, Kroldrup.
Ref: M Halsey (Lancashire).