Everton: Howard; Hibbert, Yobo, Jagielka, Baines, Osman, Neville, Fellaini (Cahill, 60), Castillo (Gosling, 60), Pienaar, Saha (Vaughan, 60).
Unused subs: Nash, Lescott, Rodwell, Baxter.
City: Given; Richards (Fernandes, 57), Onuoha, Dunne, Bridge, De Jong, Kompany, Elano (Evans, 88), Ireland, Robinho, Caicedo (Petrov, 84).
Unused subs: Hart, Bojinov, Garrido, Berti.
Goals: 0-1 Robinho (35), 0-2 Ireland (53), 1-2 Gosling (90+4).
City: Onuoha, Elano.
Referee: Alan Wiley.
Robinho was straight into action, getting among the Everton players and showing the terrier-like qualities that maybe surprised a few fans down at Arsenal a couple of weeks ago. Everton's first corner came to nothing, but the Goodison crowd were up for it and urging them on.
There was the promise of a good old-fashioned midfield scrap between Vincent Kompany and Fellaini, who has become a key player for Everton and earned wide respect after the initial ridicule directed at his haircut.
Robi surged into the penalty area after being fed by Stevie Ireland, and the Brazilian went past Tony Hibbert after a few stepovers but tumbled under Leon Osman's challenge, deemed to be perfectly fair by referee Alan Wiley.
Kompany's long diagonal pass brought Robi back into the game and his lay-back for Nigel de Jong looked tempting, but the Dutch midfielder hit it leaning back and the ball comfortably cleared Tim Howard's bar.
Louis Saha gave Shay Given his first proper save with almost 15 minutes gone, but his driven effort from a tight and distant angle presented no problem for the City goalkeeper.
City were prevented from taking a 25th-minute lead by a great save from Howard, who produced an unorthodox reflex punch to deflect a goal-bound effort by Robinho after the Brazilian and Wayne Bridge had combined down the left flank to set up a shot by Elano that was blocked by Leighton Baines.
Everton were producing the odd flash of fluent football without worrying Given unduly, but they were grateful to Baines for a brilliant tackle on Ireland in front of goal that almost certainly stopped City going ahead.
Hibbert had his hands full with Robinho but was sticking at his task, while Fellaini was everywhere to make the telling tackle and prevent City from flowing as they would have liked.
But when the sun is shining, the boys from Brazil are in their element, and City's dynamic duo made the breakthrough after 34 minutes. Elano delivered a fine long pass for Robi to take on Jagielka and fire through Howard's legs for his 14th goal of the campaign and 13th in the League.
It left Robinho just two goals behind Nic Anelka in the Premier League scoring charts - not bad for a player deemed in some quarters to have under-performed.
Howard momentarily lost his cool just before the break, dragging down Robinho by his shirt as the forward tried to go past him having not realised he had been flagged offside, but referee Wiley chose not to pursue the matter.
Given came up with a simply superb save five minutes after the restart to prevent Everton equalising when Steven Pienaar's cross was brilliantly controlled then volleyed from close range by Fellaini. Given showed why Mark Hughes shell out to bring him from Newcastle with a world-class reaction save to stun home fans.
Then City delivered a second blow to the Cup finalists when an Everton attack faltered and City broke with pace through Caicedo and Robi, who waited for Ireland's well-timed run then gave him a peach of a pass that the the midfielder almost nonchalantly stroked past the advancing keeper.
Richards had to be helped off immediately after the goal, limping and clearly in some distress, but the City travelling army were in fine spirits as they anticipated the first away win in the League since August and only the second of the season on English soil.
Everton were really up against it when England defender Jagielka was carried off after 63 minutes, having jarred his knee when he caught his studs in the turf - David Moyes had just thrown on three subs minutes earlier, so that left the home side to see out the game with ten men.
Their frustration started to show and tempers frayed between Everton skipper Phil Neville and Nedum Onouha, who were both cautioned for a touchline confrontation, before Elano joined them in the book for clattering Pienaar from behind.
Robinho skated past two tackles to reach a great position only to present an easy save to Howard, and Everton fans tried to lift their side to an heroic finish as the last 15 minutes arrived.
But that was too tall an order for Moyes' ten men, even if Richard Dunne did almost give his old club a goal by default when he back-headed Pienaar's free kick close to his own post as the clock ticked down, and eager Robi clipped the outside of a post before the end from an astute ball by Ireland.
But Everton rallied when the referee decided to add a remarkable seven minutes of stoppage time, and sub Dan Gosling ensured a nailbiting finish in the fourth of those by firing Pienaar's pass beyond Given.
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