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.
GEAR:Save 10% on new Man United home and away kits. Free delivery on orders over £50
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.
With the match heading for a penalty shootout, United cleared a corner and confusion in the City defence allowed Nani to race clear, round Hart and slot the ball calmly into an empty net.
"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."
United started brightly, new winger Young combining well with strikers Wayne Rooney and Danny Welbeck as big-spending City failed to settle.
Rooney fired a free-kick inches wide and tempers flared with a succession of clumsy challenges before Lescott rose above a static defence to grab the opening goal against the run of play on 38 minutes.
IMMEDIATE IMPACT
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.
Ferguson made three substitutions at half-time, replacing experienced defenders Rio Ferdinand and Nemanja Vidic, and the changes made an immediate impact.
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.
Deep into stoppage-time Dzeko missed a chance from a corner and Rooney hoofed the ball down field.
City defender Vincent Kompany hesitated and Nani nipped in, took advantage of a favourable ricochet and gleefully grabbed the winner.
"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."
