MANCHESTER - Everton striker Ayegbeni Yakubu took his tally for the season to 16 goals to keep the club's Champions League dream alive.
Yakubu made the breakthrough in the 30th minute and Joleon Lescott added a second eight minutes later.
It meant Everton regained fourth spot from Liverpool after stretching their unbeaten run in the top flight to seven games.
City's misery was complete in stoppage time when Martin Petrov was sent off for kicking out at Leon Osman.
England manager Fabio Capello continued his tour of top grounds by taking in the game and saw Everton dominate the first half.
City looked nothing like the side that defeated Manchester United and were lacking in ideas.
Everton almost made the breakthrough in the sixth minute following a sweeping move.
Lee Carsley started it and found Steven Pienaar on the left. He delivered a pin-point cross into the area.
Yakubu lost his marker but goalkeeper Joe Hart did enough to put him off and the ball drifted out of play for a corner.
A minute later Everton had claims for a penalty dismissed by referee Rob Styles when a shot from Tim Cahill came off the elbow of Micah Richards.
The visitors came close to opening the scoring in the 28th minute when Pienaar latched onto a pass from Cahill.
He cut inside and steered his effort beyond Hart only to see it come back off the post.
Everton's pressure paid off after 30 minutes when Yakubu made the breakthrough.
Cahill showed good skill in the area and released the Nigerian, who prodded the ball home.
Everton made it 2-0 eight minutes later when Lescott got goal-side of Richard Dunne to head in a cross from Lee Carsley.
Carsley deserves enormous credit after chasing a lost cause and delivering a marvellous ball to the back post.
City looked stunned and were heading for a second successive home defeat after losing to Arsenal.
Everton were playing fluent football going into half-time and running the midfield.
They started the second period going forward with Phil Neville rifling a shot over the bar in the 47th minute after being set up by Pienaar.
Elano then knocked the ball into the path of Darius Vassell and he tried to send Benjani Mwaruwari away.
However, with the rain sweeping across the stadium, the ball skidded on the greasy surface and away from him.
Everton almost made it 3-0 in the 54th minute after some sloppy defending by City.
Yakubu got the better of Micah Richards and found Cahill in the six-yard area but his shot was cleared off the line by Dunne.
City had increased the tempo and were playing with more confidence but still finding Everton hard to break down.
Petrov tried his luck after 64 minutes but his powerful effort from 20 yards was blocked by Carsley.
City were growing increasingly anxious and Dunne headed a free-kick from Elano over the bar.
Play broke back down the other end and Everton made another unsuccessful penalty claim four minutes later.
Richards was again involved and clearly handled Lescott's throw-in. However, referee Styles opted to award a free-kick on the edge of the area.
Osman whipped in a vicious shot that Hart did well to beat away before City scrambled the ball clear.
Everton were carving out numerous chances and Hart stood tall to block Johnson's effort in the 84th minute before Petrov was sent off for a moment of madness.
