The big pre-match news was City boss Manuel Pellegrini kept faith with the out-of-sorts Joe Hart, despite making six changes from his line-up that lost to Bayern Munich in midweek.
And it looked to have backfired on the Chilean as early as the 16th minute when Everton took the lead.
A mix up between City defenders Joleon Lescott and Vincent Kompany allowed Romelu Lukaku to beat the offside trap and he fired the ball under a flailing Hart to put the visitors ahead.
However, only a minute later, City were level thanks to Alvaro Negredo.
A classy pass from Yaya Toure created the opening for the Spaniard, who finished coolly past Everton keeper Tim Howard.
On the half hour, City were rocked by a fresh injury setback to skipper Vincent Kompany. He was substituted for Matija Nastastic with a suspected thigh strain.
The hosts were in front a minute before halftime thanks to a wonder goal from Sergio Aguero.
City put the game beyond Everton just before the 70th minute mark after Pablo Zabatela won a penalty for a foul from Coleman.
Aguero converted the spotkick, but only after Howard had managed to palm his shot onto the post before it rebounded off his head and over the goalline.
The match quickly petered out with City keeping control of possession. Lukaku's substitution summed up Everton's play in the second-half.
The visitors tested City in the opening 45 minutes, but struggled to make an impression after the break, despite the hosts' loss of skipper Kompany.
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