After a goalless first half, Ezin Dzeko headed the German champions into the lead, only for Ryan Giggs to equalise with a deflected free-kick and Michael Carrick to grab the winner with a superbly-crafted goal.
United started with Michael Owen in attack alongside Wayne Rooney while Tomasz Kuszczak took over from Ben Foster in goal.
Wolfsburg opted to begin with Grafite and Dzeko in a two-pronged attack so former Newcastle United star Obafemi Martins had to settle for a place on the bench.
Wolfsburg, currently sixth in the Bundesliga table, five points behind early leaders Hamburg, started tidily and dominated the opening 20 minutes.
Poor play by Nemanja Vidic allowed Zvjezdan Misimovic a sniff of goal but his effort was dealt with by Kuszczak.
Patrice Evra then gifted possession to Dzeko who lashed his ambitious effort well wide before another mistake, this time by Rio Ferdinand, allowed Christian Gentner to have a shot, but he mis-hit it terribly.
The game changed in the 20th minute though when Owen limped off with a recurrence of his groin strain and was replaced by Dimitar Berbatov and his guile immediately lifted United.
Six minutes after coming on, a lovely touch by the Bulgarian set up Antonio Valencia who dragged his shot wide when he should really have got the effort on target.
Just past the half-hour mark Berbatov, again, played in Carrick who tried to lift the ball over Diego Benaglio only for the Wolfsburg keeper to be alive to the danger as he blocked the effort.
Back game the visitors and, in the 35th minute, the outstanding Misimovic's corner was met by Gentner but his powerful header flew over the crossbar.
At the start of the second half a Wolfsburg corner again caught United out and, although Miguel Ricardo Costa got a powerful connection to the ball, he was unable to guide it goalwards.
The Bundesliga side took the lead in the 55th minute when the Japan international Makoto Hasebe crossed the ball over to Dzeko at the far post and he rose above Evra to head home.
However, just four minutes later United were level. Giggs' free-kick took a massive deflection off the wall, wrong-footing Benaglio as the ball ended up nestling in the back of the net.
With 12 minutes left United grabbed their winner when Rooney, Berbatov and Giggs all played their part in setting up Carrick who curled a lovely shot home from the edge of the area.