Manchester City ended Everton's unbeaten record in the Premier League to finish a difficult week on a high.
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Defeats by Aston Villa and Bayern Munich had made this a very important game for City and under-pressure goalkeeper Joe Hart, and they responded in style with a 3-1 win at the Etihad Stadium.
Romelu Lukaku put Everton ahead in the 16th minute but Alvaro Negredo equalised a minute later and Sergio Aguero struck to give the hosts the lead just before half-time.
The unlucky Tim Howard then diverted in a third in the 69th minute after initially saving Aguero's penalty.
The victory was only City's third in 13 attempts against Everton, who tasted defeat for the first time in the league under Roberto Martinez.
Despite his refusal to confirm that Hart would start following his mistakes against Bayern, City boss Manuel Pellegrini showed faith in the England man while changing more than half his team.
Only Vincent Kompany survived from the defence that faced the European champions while David Silva, James Milner and Negredo were also included.
Everton boss Martinez was without on-loan Gareth Barry, ineligible against his parent club, and the Toffees missed the midfielder's calm presence in a frenetic first half.
Hart was straight into the action, diving on a ball from Steven Naismith with Lukaku lurking, but it was City who had the best of the early chances.
In the fifth minute, Howard pushed a shot from Yaya Toure behind, while two minutes later half the crowd thought the hosts had taken the lead when Aleksandar Kolarov's free-kick flew into the side-netting.
But it was Everton who made the breakthrough in the 16th minute, and again there were questions over Hart.
A long ball from Phil Jagielka beat the City defence rather too easily and Lukaku broke into the area before placing a shot under Hart's right hand.
The Toffees had no time to enjoy their lead, though, as from the restart City poured forward and Toure played in Negredo, who beat Howard.
There was no let-up in the pace of the game, and it was the hosts who were doing most of the pressing.
Milner's deflected cross hit the outside of the near post while in the 26th minute Aguero missed a clear chance when he shot wide after being played in by the impressive Silva.
City were dealt a blow in the 35th minute when captain Kompany limped off to be replaced by Matija Nastasic.
The Serbian's first act was a risky push in the back on Lukaku in the area but referee Jon Moss waved away muted penalty appeals.
It had not been Aguero's day, the Argentinian unusually clumsy in the final third, but he showed the sort of clinical touch for which he is renowned to give City the lead in the 45th minute.
Silva was the architect, the Spaniard's precise pass helping Aguero, who was just onside, beat former City man Sylvain Distin and tuck the ball into the far corner.
Aguero could even have had another before half-time after being played clean through by Toure's chipped pass but Jagielka got back to deny the striker.
City were keen to add a third and pressed hard at the start of the second half without creating a real chance.
Everton hit their hosts on the break with a fine ball from Ross Barkley putting Kevin Mirallas through but the Belgian's first touch was too heavy and Hart was able to pounce.
Kolarov, who had been having an influential game, was forced off in the 58th minute after suffering a cut to his forehead when he was nudged into a collision with Nastasic by Naismith.
City were in the wars, with Pablo Zabaleta also taking a bang that drew blood, but with cotton wool up his nose he returned to the pitch and promptly won a penalty.
Seamus Coleman leant into the full-back, who seemed to go down easily, and Everton were furious with Moss' decision.
Aguero stepped up and Howard tipped his shot onto a post but the ball hit the keeper in the back of the head on the rebound and went in.
Martinez had sent on Darron Gibson and Gerard Deulofeu for Leon Osman and Mirallas but Everton could not put any real pressure on Hart.
City continued to look the side more likely to score and Howard prevented Negredo from making it four with a smart stop before also denying substitute Samir Nasri in injury time.