Captain Leon Osman put them in front before the break, but it looked as though it was going to be tough remaining 30 minutes when Steven Pienaar was handed his marching orders for a foul on Javi Garcia.
However, the home side defended stubbornly before Nikica Jelavic sealed the win in stoppage time.
Sports Mole looks back over the action to determine if Everton were worthy winners.
On target 5
On target 11
Was the result fair?
A combination of Everton playing extremely well and Man City not being at the races means that the home outfit were deserving winners. In every aspect they were better than the champions and eventually recorded the result that their performance warranted.
David Moyes demanded a big display from his players and he got that. From the very first whistle his team hunted their opposition in packs and won the ball back quickly. Then, when they did have possession, their passing was crisp and they got themselves into numerous dangerous positions. If they can keep that up between now and the end of the season, they will have a real chance of qualifying for the Europa League.
Man City's performance
With the Premier League title on the line, you would have expected Man City to be up for this match. As it was, there looked to be little desire about the visitors. There was no tempo about their play and regardless of the system, there is no excuse for poor passing and a lack of effort.
Sports Mole's man of the match
Seamus Coleman: The Irish full-back joined Everton from Sligo Rovers for around £60,000 and he looks an absolute bargain buy on today's evidence. During the first half the full-back proved himself to be a decent attacking force, but after his side lost Pienaar, he played a major role in keeping Man City at bay.
On this occasion this award is not going to a player, but to City manager Roberto Mancini. He started with a 3-5-2 formation and at times his players did not seem to know where they were meant to be. Their lack of width was punished time and again by Leighton Baines and Coleman. It also took the Italian boss until the 82nd minute to change his team's shape.
It looked as though Lee Probert struggled with the pace of today's match. During the first half he was far too card happy and never allowed the play to flow. Although he got the decision correct to send off Pienaar, he made an horrendous error when awarding Man City a free kick when it should have been a penalty for handball against Marouane Fellaini.
Everton: Following next weekend's international break, the Toffees are at home again on Saturday, March 30 when they welcome Stoke City to Goodison Park.
Man City: On the same day City will play host to Newcastle United at the Etihad Stadium.