The Portugal playmaker broke clear from the halfway line in the fourth minute of time added on to follow up his sublime equaliser earlier in the second half.
City had capitalised on two David de Gea errors to go ahead through Joleon Lescott and Edin Dzeko but Chris Smalling halved the deficit after the break.
Champions United made the better start and debutant Ashley Young had an early shot deflected wide by England team-mate Lescott. Wayne Rooney headed back across goal from the resulting corner and Nani mishit a shot straight to Smalling but the defender could only side-foot at goalkeeper Joe Hart.
City emerged unscathed from that early pressure to snatch the lead after 38 minutes through Lescott. The defender got between Rio Ferdinand and Nemanja Vidic to glance a header from a David Silva free-kick past static debutant goalkeeper De Gea from six yards.
Worse was to follow for De Gea as Dzeko tried his luck from 25 yards and saw his low shot beat the Spaniard.
United got themselves back into the game after 52 minutes, however, when Smalling got forward to turn in a well-flighted free-kick from Young on the six-yard line.
United poured forward again and claimed a superb equaliser after 58 minutes as Nani twice played a part in an intricate move involving Rooney and Tom Cleverley and broke forward to clip the ball over Hart.
Rooney blasted over from inside the area as United upped the tempo further. United had another opportunity after Smalling broke down the right but Nani's shot was blocked by Lescott and Cleverley fired over.
It seemed like the game would be settled by a penalty shootout but United snatched victory in stoppage time after Vincent Kompany was caught in possession on the halfway line by Nani. The 24-year-old raced clear and calmly took the ball around the advancing Hart.
Source: PA
Source: PA