United needed to pick up a point in Germany to secure a potentially easier first knockout round opponent and Owen came to the rescue on a night where they were second best for long periods of the game.
Missing 12 first-choice players through injury, the Red Devils were a pale imitation of their best and offered little as an attacking force until Owen broke the deadlock in the 44th minute.
Midfield trio Ji-sung Park, Michael Carrick and Darren Fletcher made up the back-four alongside Patrice Evra and unsurprisingly it was the home side who looked most likely to make a breakthrough.
Andrea Barzagli and Zvjezdan Misimovic should both have converted headed chances in the opening 20 minutes as United's patched up defence looked at sixes and sevens.
Tomasz Kuszczak did well to nudge Makoto Hasebe's powerful 20-yard shot over his crossbar with an outstretched fingertip, before Owen popped up with the first goal of the game on the stroke of half-time.
The composed Paul Scholes fed Nani and the elusive Portugal winger's pinpoint cross was headed into the bottom corner of the net from eight yards by the unmarked Owen.
It didn't take Wolfsburg long to breach the nervy United backline as star striker Edin Dzeko scored a virtual repeat of the Owen opener just eight minutes into the second half.
The German champions needed to win to be sure of their own progress and they dominated possession as the second half wore on.
But after Kuszczak clawed away shots from Grafitie and Dzeko as the home side looked to turn the screw, United and Owen left them stunned with an 83rd minute second of the night.
Lively substitute Gabriel Obertan tricked his way past two defenders before picking out Owen, who had the simple task of diverting the ball over the line from close range.
Owen was denied a hat-trick when goalkeeper Diego Benaglio stood up well to prevent him notching a killer third when one-on-one soon after.
Wolfsburg should have been back on level terms in stoppage time when Sascha Riether took a swipe at fresh air when the ball was cut back from the left byline.
To compound the home fans' misery, Obertan then fed Owen who did claim his hat-trick after closing in on goal before dinking a cool finish over the diving goalkeeper with virtually the final kick of the match.
The result sent United through to the last 16 as one of the top seeds, while Wolfsburg will have to be content with a place in the Europa League after CSKA Moscow's 1-1 draw with Besiktas sent the Russian club through as group runners-up.