Robinho scored one and created another as Manchester City's bid to finish seventh and secure Europa League qualification gathered pace at Everton.
The Brazilian opened the scoring just after the half hour, latching on to Elano's through ball and clipping in.
And he then played in Stephen Ireland to wrap up the victory, the midfielder slipping past Tim Howard from 16 yards.
Dan Gosling swept in a consolation late on, but a bad injury to Phil Jagielka did much to sum up Everton's day.
It means the Toffees miss the chance to jump up into fifth, with Aston Villa only managing a draw away to Bolton.
But for City manager Mark Hughes the win will come as a welcome relief, having recently faced questions about his future thanks to his side's Jekyll and Hyde form this campaign.
While 11 victories at home is a record bettered only by local rivals United, one success on their travels before today has ensured Hughes's outfit has yo-yoed around mid-table all campaign.
Everton manager David Moyes:
"We're disappointed but the players have put in a great effort in recent weeks so maybe this was going to be on the cards. There was a bit of fatigue there.
"We've conceded two counter-attacking goals and not defended particularly well - we needed to hang in a bit more at 1-0 and once the second went in we were always going to struggle. "Unfortunately, too, the news is not good on Jagielka. I'd say it's more doubtful than hopeful that he'll play in the Cup final."
Man City boss Mark Hughes:
"I thought we were really good value for the win today. There was a real focus to our play, we were dynamic and our determination shone through.
"Yes, it was possibly a good time to play Everton, but that shouldn't take anything away from our win - we deserved it.
"To be honest we could, and probably should, have won by more because I thought we were very comfortable.
"Robinho was excellent today, not just for the goals but his all-round game, and he is really hitting some form for us. He's had some stick this season but his play - and that of Ireland's - was outstanding."
Everton: Howard, Hibbert, Yobo, Jagielka, Baines, Osman, Neville, Castillo (Gosling 60), Pienaar, Fellaini (Cahill 60), Saha (Vaughan 60).
Subs Not Used: Nash, Lescott, Rodwell, Baxter.
Booked: Neville.
Goals: Gosling 90.
Man City: Given, Richards (Fernandes 57), Onuoha, Dunne, Bridge, De Jong, Kompany, Elano (Evans 88), Ireland, Robinho, Caicedo (Petrov 84).
Subs Not Used: Hart, Bojinov, Garrido, Berti.
Booked: Onuoha, Elano, Fernandes.
Goals: Robinho 35, Ireland 54.
Att: 37,791
Ref: Alan Wiley (Staffordshire).
www.bbc.co.uk
'
West Ham U. 0 - 1 Chelsea
0-1 S. Kalou 55. min.
,
Barnsley 1 - 1 Wolverhampton W.
1-0 J. Macken 58. min.
1-1 K. Reid 84. min.
,
Southampton 2 - 2 Burnley
1-0 B. Wright-Phillips 11.min.
1-1 G. Alexander (pen.) 32.min.
2-1 D. McGoldrick 44. min.
2-2 C. Carlisle 67. min
