Fellaini headed the Toffees, victors in eight of their previous 10 clashes with City, into a first-half lead but then conceded a controversial penalty to allow Carlos Tevez to level.
Everton felt Edin Dzeko had gone to ground too easily to win the award but Tevez made no mistake and City went on to dominate the second half.
The result preserved City's unbeaten start to the season in the Premier League and prolonged their run of home games without defeat to 37, a sequence stretching back to a loss to Everton two years ago.
Tevez controlled well in the area but was unable to shoot and Dzeko inadvertently took the full force of a Samir Nasri shot in the back of his head.
Everton's 33rd-minute opener came in familiar fashion as the ever-dangerous Leighton Baines, who passed a fitness test to feature, crossed and Fellaini eventually headed in.
Vincent Kompany did well to divert the cross away from Nikica Jelavic but it dropped for Fellaini, who headed home at the second attempt at the far post after Joe Hart saved his initial effort.
That brought the game to life and City almost found an immediate equaliser as Tevez met a Nasri cross with a deft header that Howard did well to save.
Then Dzeko tangled with Fellaini and went to ground. Referee Lee Probert sparked immediate protest from Everton by pointing to the spot and Toffees manager David Moyes clearly thought the award was harsh.
Tevez made no mistake as he stepped up to tuck home his eighth of the campaign.