City defender Joleon Lescott and striker Edin Dzeko scored late in the first half to stun Premier League champions United, who had dominated the early stages of the traditional season curtain-raiser against the FA Cup winners.
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United responded quickly after half-time, however, defender Chris Smalling steering Ashley Young's free-kick past Joe Hart from close-range and Nani finishing off a superb intricate passing movement with a deft chip from a narrow angle on 58 minutes.
"It was a very good performance in terms of our football," United manager Sir Alex Ferguson told Sky Sports. "I couldn't believe we were 2-0 down at halftime but goals change games. The players kept their heads, played their football and got the result they deserved."
The shell-shocked United defence then failed to close Dzeko down and the Bosnian's fizzing long-range drive flew past goalkeeper David de Gea who reacted too slowly to attempt a save.
Young's free-kick was neatly prodded home by Smalling and United unlocked the City defence again when Rooney and substitute Tom Cleverley exchanged neat passes to set up Nani's sublime finish.
United continued to dominate possession but City's greater strength in midfield kept them in the match and they always posed an aerial threat from set-pieces.
"We always believe we can win until the last minute," said the Portuguese winger who was named man of the match. "It is good to beat Manchester City like that."
