Former Manchester United midfielder Darron Gibson allowed his old club to go level on points at the top with City via his brilliant 60th minute strike as the Toffees kept Roberto Mancini's men to just three shots on target, their lowest total of the season.
It was a strong performance from Moyes' men, who could now celebrate the arrival of new striker Nikica Jelavic, and despite having much less possession the Toffees were able to see it through with goalkeeper Tim Howard having very little to do in comparison to most keepers who take on City.
The only goal of the match came on the hour-mark when Landon Donovan teed up fellow January signing Gibson, after Leighton Baines' cross from the left fell to the American, and the Republic of Ireland international struck a slightly deflected shot with the outside of his boot past Joe Hart from the edge of the area.
Earlier in proceedings, the impressive Denis Stracqualursi saw his goalward header cleared off the line by ex-Toffees defender Joleon Lescott before Samir Nasri's long range screamer was only denied by the corner of Howard's crossbar.
As for out and out scoring chances, there were not too many to write home about but one thing worth noting was the added time required in the first half was due to one fan handcuffing himself to the post of Everton's goal with a few Toffees players surrounding him to see what the problem was.
It only took minutes for the stadium officials and police to get rid of the disturbance and let the Toffees get on with yet another victory over City to make it eight from their last ten meetings against Roberto Mancini's charges.
TRIBAL ASKS: Can a win such as this, plus the signing of Jelavic, give Everton the kickstart they need to push well into the top half of the table?
Goodison Park, Liverpool - 29,856