Everton had won on their last four visits to City - and for an hour frustration was in the air again as they mounted a wall of well-organised resistance that kept Roberto Mancini's side at bay.
The introduction of substitute Mario Balotelli on the hour led to the breakthrough as he scored with a deflected shot after 68 minutes and finally unsettled Everton with an impressive cameo.
It was the type of result and performances that adds weight to the argument that City will mount a serious title challenge this season
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James Milner, another second-half substitute, added the second with two minutes left from David Silva's sublime pass to allow City to move top of the Premier League ahead of Manchester United's visit to Stoke City.
And it was a win City deserved for demonstrating the patience and persistence they will need as Everton's dour approach is likely to be mirrored by plenty of sides who will attempt to suppress City's wide range of attacking options at Etihad Stadium.
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Everton's tactics appeared designed to secure a draw and perhaps aim to take an isolated chance on the break.
But David Moyes' side were undermined by a failure to offer anything in attack, although substitute Louis Saha - and his manager - were rightly infuriated when referee Howard Webb failed to award a free-kick when he was blatantly fouled on the edge of the area by Vincent Kompany with the game still in the balance.
Moyes also believed Everton had been the victims of injustice in the build-up to Balotelli's crucial goal, claiming City were wrongly awarded a throw in.
Mancini will relish the manner of this win as much as other victories earned in real style this season. Everton offered a stern test and City showed growing maturity to get the three points.
Everton's superbly drilled defensive formation offered nothing other than frustration to City in the first half as they stood firm.
Moyes had clearly earmarked Silva as central to City's threat and he deployed youngster Jack Rodwell to man-mark the Spaniard. And when he received a yellow card for a foul on Silva responsibility briefly switched to Phil Neville, until he drew similar punishment from referee Webb after a clash with Silva.
Sergio Aguero was City's main threat in the early exchanges, but it was the 53rd minute before Everton posed a serious threat as Tim Cahill's header from Seamus Coleman's cross floated over the bar.
It was only when Balotelli came on for Edin Dzeko on the hour that City made serious inroads into the Everton defence. Samir Nasri had a shot well saved by Tim Howard before the Italian broke the deadlock seven minutes after his introduction.
Balotelli's finish from the edge of the area was measured and also took a decisive touch off Everton defender Phil Jagielka to send the ball tantalisingly out of Howard's reach into the bottom corner.
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The visitors now needed to shift the entire emphasis of their approach, but City were playing with renewed confidence and Silva hit the woodwork with Howard beaten.
Balotelli was then narrowly off target before setting up Silva for a tap-in, only for the goal to be ruled out for offside.
Silva was at his creative best as City wrapped up the win with one minute left. Everton substitute Royston Drenthe lost possession in midfield and Silva threaded through a perfect invitation for Milner to slide his finish past Howard.
Everton had offered next to nothing in terms of attacking threat, although another City substitute Stefan Savic made a timely intervention in injury time to clear Marouane Fellaini's shot off the line.
Live text commentary
Manchester City finally released the recent stranglehold Everton have placed on them with a hard-fought victory at Etihad Stadium.