David Moyes' side were booed off the Goodison Park pitch last time out as the Latics doled out a 3-0 thrashing, but they were at the races from the first whistle in Saturday's lunchtime kick off.
Toffees captain Leon Osman opened the scoring with a dipping left-footed strike from the edge of the penalty area, and substitute Nikica Jelavic wrapped up the points at the death with a deflected effort.
Former Everton boss Joe Royle told Sky Sports: "From the very first minute, they had intensity and pressed. Last week, you couldn't name an Everton man of the match because they were so poor - this week it's because they were all so good.
"Victor Anichebe has never played better in a blue shirt, Leon Osman was terrific and then you've got Seamus Coleman at right back. Right the way through, from one to 11, they were excellent.
"Nikica Jelavic had just one goal in 17 games prior to that, so that's coming out of a long nightmare for him. There's no doubt that Everton need him scoring goals on the run-in because he did so well when he first came. He will feel he's broken the jinx.
"The goalkeeper Jan Mucha made some saves. A couple of good ones. Goalkeepers practice it all the time getting up quickly and going to make the second save and that's what he did. It was a good brave save."
The game was not without controversy, however - Steven Pienaar shown a red card for two yellows and Marouane Fellaini appearing to handle the ball in the box with the score at just 1-0.
Referee Lee Probert seemed to rule that Leon Osman was guilty of handball before the ball reached Fellaini, ultimately awarding City a free-kick outside the Toffees area.
Glenn Hoddle said of the incident: "He's got the best eyesight I've ever seen in my life. Everyone expected the handball was on Marouane Fellaini inside the penalty area which could have been a second sending off as well.
"How he sees Leon Osman has thrown himself I don't know. Osman was great today and it sums him up that he was trying to get the block in himself.
"If you just see as he made his decision, the referee just put his arm up as if to say it was Fellaini. It was a key decision."
Royle added: "In real time, it looked like Fellaini was jumping out of the box and was running towards the ball, so it's a hard call for the referee.
"I think he's not sure. He knows it's a handball but he's played on the safe side of staying alive!"
The win keeps Everton well and truly in the hunt for fourth place and Champions League football.