Under-fire City manager Stuart Pearce may have kept the dissenting voices at bay with his side's 2-0 win against West Ham last week, but he must have been weary of unbeaten Everton's threat to his future employment prospects.
Though David Moyes will be pleased with his rejuvenated side's start to the season, he was desperate to consolidate Everton's position in the league with a home win before the international break.
Mikel Arteta won a dangerous free-kick in the seventh minute after a clumsy Ishmael Miller trip, but the Spaniard shot straight into the wall.
The opening exchanges were pretty even and uninspiring as both teams probed without forcing the pace too much and Sylvain Distin keeping an in-form Andrew Johnson under control.
Georgios Samaras nearly sprung Everton's offside trap on 15 minutes, but unlike the assistants at Newcastle last week, the linesman raised his flag much to the home crowd's relief.
Everton won a corner a minute later after Richard Dunne was forced to head over his own goal, but the resulting effort was well cleared.
Johnson had the first clear chance of the game after a fine cross by Nuno Valente on 20 minutes, but his header went straight into Nicky Weaver's hands. Moments earlier Joleon Lescott made a rare error that almost let City in before Everton broke.
Phil Neville gave away a dangerous free-kick when he hauled down Miller on the edge of the box, but Joey Barton's effort ricocheted off Leon Osman and was gathered by a grateful Tim Howard.
A Barton inspired City were beginning to apply themselves rather well midway through the half without ever really threatening the Everton goal.
The home side sensed the crowd's discomfort and duly stepped up their efforts with three chances in as many minutes, with a lovely James Beattie effort ruled out for a foul and Johnson missing the City goal by inches.
Beattie should have scored on 43 minutes after Johnson shrugged off Miller to put in a perfect cross, but such is the former Southampton man's anxiety in front of goal, he could only snatch at it.
A minute later, Everton were in front after Neville floated in a cross for Everton's record signing Johnson to volley past Weaver via a glancing deflection from Miller.
Everton came out bristling with confidence and almost carved out a real opening in the 46th minute as Arteta robbed an otherwise excellent Dunne and passed to Johnson, but the ball eluded the striker as he closed in on goal.
Weaver stopped a double strike from Osman after lovely work by Valente, who dispossessed Distin and played a dangerous ball into the City area.
At the other end Dietmar Hamann shot just past Howard's post from 20 yards.
Beattie managed to clear over his own bar as a wicked Barton corner caused consternation among the Everton defence.
A wild Dunne deflection almost fooled Weaver after Beattie shot and the ball spun high into the air off the Irish international and nearly dropped into his own net.
Bernado Corradi replaced Stephen Ireland on 58 minutes as Pearce looked to add more bite to his side in the second half.
Samaras should have done better on the hour, but could only shoot tamely at Howard as Joseph Yobo closed down well.
Everton should have been two up after an Arteta shot which Weaver could only parry to Johnson, whose shot was blocked on the line by a diving Dunne.
Everton players appealed for handball but referee Alan Mariner was having none of it. A minute later, Samaras had the chance to level but his shot was well off-target.
Youngster Victor Anichebe came on for Beattie on 81 minutes and immediately earned a corner though Arteta's kick came to nothing.
Everton were almost the victims of another two dodgy decisions within seconds as a clearly offside Corradi almost scored but for a last-ditch Valente tackle.
Arteta was clean though at the other end when the ref inexplicably pulled up play for an earlier foul on the Spaniard and surely the advantage should have been played.
City then scored with the final kick of the game to break Everton hearts, as Micah Richards took advantage of a melee in the area to hit an unstoppable shot in off the underside of the Everton bar.