Owen headed home Nani's cross on the stroke of half-time, and after Wolfsburg rallied through Edin Dzeko on 56 minutes the nimble forward slotted home seven minutes from full-time and sealed the win with a crafty finish in added time to send the English champions through as Group B winners.
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Injury-hit United, fielding just one recognised first-team defender in French international Patrice Evra, rode their luck at times, although Wolfsburg only had themselves to blame for failing to take several excellent chances against United's makeshift defence which featured regular midfielders Michael Carrick and Darren Fletcher.
A decent penalty claim was dismissed early in the first half when Makoto Hasebe was upended by Carrick, while Andrea Barzagli and Zvjezdan Misimovic missed excellent chances.
Wolfsburg's consolation is a Europa League last 32 knockout stage place after finishing third in the group.
United manager Alex Ferguson was delighted after Owen's match-winning performance.
"Fantastic. Brilliant. You know what he is. His timing of runs is fantastic," he told Sky Sports.
