City led 2-0 at half-time but Chris Smalling pulled one back, Nani equalised with a sublime finish and the Portuguese winger struck again deep into stoppage-time as the Premier League champions avenged last season's FA Cup semi-final defeat by their neighbours.
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"It was a very good performance in terms of our football, I couldn't believe we were 2-0 down at half-time," United manager Sir Alex Ferguson told Sky Sports.
"But the players kept their heads, kept playing football and got the result they deserved. They have courage to keep the ball and are not admitted by tough tackling."
Ferguson's United have made a habit of coming from behind to snatch important victories and the catalyst against City was the manager's decision at half-time to replace the experienced Rio Ferdinand, Nemanja Vidic and Michael Carrick.
New signing Phil Jones, Jonny Evans and young midfielder Tom Cleverley were thrown into the fray and their energy and enthusiasm were vital as United tore into the City defence.
"The difference the young lads made was outstanding," United striker Wayne Rooney said.
"We never know when a game is finished. Of course they are going to try and fight us for the title. They scored two goals from nowhere but we showed character to win the game."
TACTICAL AWARENESS
Ferguson has so far failed to sign a replacement for the retired Paul Scholes but the 21-year-old Cleverley's neat distribution and tactical awareness hinted that he could provide at least a temporary solution.
One concern for Ferguson was the performance of his new Spanish goalkeeper David de Gea who was stranded when Joleon Lescott nodded in David Silva's teasing free-kick and slow to react when Edin Dzeko's ambitious 30-metre strike flew past him just before half-time.
"It was bending a bit, it's difficult to say if he should have done better," Ferguson said.
City manager Roberto Mancini, charged with the task of ending United's domination of English football and bringing the league title to the club for the first time since 1968, admitted his side had been outplayed.
"They were better than us but sometimes in football if you cannot score you give the other team a chance. We were 2-0 up so it is not good to lose from this position."
United begin the defence of their Premier League title at West Bromwich Albion on Sunday, while City, whose expensive new striker Sergio Aguero was an unused substitute in the Community Shield, host promoted Swansea City next Monday.
