Superb second-half headers from Sylvain Distin and Leon Osman gave Everton a seventh win in eight meetings against Man City.
With David Silva at his influential best, City seemed in little trouble as they dictated play in the opening 45 minutes, were they squandered several chances at Goodison Park and were stunned when Sylvain Distin cancelled out Yaya Toure’s first-half opener in the 66th minute and six minutes later, Leon Osman scored a fantastic winner.
The visitors looked composed in possession early on, with Silva exhibiting some sublime touches. He went close after brilliantly controlling a hopeful punt from Vincent Kompany and beating Tony Hibbert to shoot across goal, earning applause from the Everton crowd.
He showed more skill when he tapped a James Milner cross into the six-yard box but Patrick Vieira volleyed over.
Milner found space in the area as Everton pushed up but he opted to pass instead of shooting and the hosts got back to clear.
The respite was shortlived for the hosts, however, as City claimed the lead moments later, in the 28th minute.
Silva was again the orchestrator, although he benefited from a lucky ricochet as he took the ball past Distin.
He found Toure unmarked to his right and the Ivory Coast international powered forward to clip the ball over Tim Howard.
The visitors paid the price for their profligacy as Everton equalised in the 66th minute through Distin.
Everton had sent on Tim Cahill – scorer of five goals against City – just moments earlier and the Australian went straight into the box for an Arteta free-kick.
Introducing the Everton Mishmash!
But it was Distin who did the damage, rising at the far post to power a header into the bottom corner which Joe Hart failed to keep out.
The goal infused Everton with confidence and Beckford went through.
The striker was ruled marginally offside and chipped wide anyway, but nevertheless it was a warning for City.
It was one they failed to heed as the Toffees grabbed a second in the 72nd minute.
Neville delivered an inviting cross into the area and Osman timed his leap superbly, beating Kompany in the air and glancing a looping header over Hart into the top corner.
It almost got worse for City as Beckford shot straight at Hart from close range.
City´s frustrations were perhaps evident at the final whistle as Cahill and Kolarov appeared to argue with each other while Neville exchanged words with the visitors´ assistant boss Brian Kidd.