Fresh from his hour's spell at centre-half against West Ham on Saturday, Carrick struggled with Dzeko's 6ft 4in frame at the start and was lucky not to concede a penalty for a mis-timed tackle on Makoto Hasebe.
More wobbles followed with Andrea Barzagli and Zvjezdan Misimovic both heading wastefully over the bar from good positions.
It was hard work for the visitors on a heavy pitch, but there was a glimmer of hope on the half hour when Danny Welbeck slotted in smartly only to see the offside flag raised.
One minute before half-time the United faithful were jumping up and down celebrating a very well-worked opening goal.
Paul Scholes swept the ball to Nani on the left and the Portuguese star looped his cross to the back post for Owen to nod in for his second goal of the Champions League campaign.
With third-placed CSKA Moscow leading at half-time it was crucial the Germans got back into the game and 10 minutes into the second-half that is exactly what they did.
Lively midfielder Schafer burst down the left to cross in for the unmarked Dzeko to power a header past Tomasz Kuszczak.
A more conservative United invited Wolfsburg to push forward and their innovation was almost rewarded with a stinging shot from Brazilian striker Grafite palmed away by Kuszczak.
Manager Sir Alex Ferguson brought on Antonio Valencia and Gabriel Obertan to shore up the tiring midfield and with eight minutes remaining United shocked the hosts to take the lead.
Obertan had been on the pitch for eight minutes and he danced his way through the defence to pass the ball across the six-yard line for Owen to poke home.
Following a goalmouth scramble at the other end, there was still time for the red shirts to break away and it was Owen again - still pushing hard for an England recall - who chipped calmly over the keeper.
Job done for the Old Trafford side and Ferguson's selection headache will at least subside for a few days before their Premier League commitments kick into action again at the weekend against Aston Villa.
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