United had 12 first-teamers out of action and had their backs against the wall early doors in the Volkswagen Arena.
But they took the lead on the stroke of half-time through Owen’s header from a brilliant Nani delivery.
The Germans went on to equalise early in the second half thanks to a bullet header from Edin Dzeko, but Owen popped up again with seven minutes remaining after brilliant play by substitute Gabriel Obertan.
And he netted again in the final minute to earn United a fine away victory and condemn the Germans to third place in the group and Europa League football.
It was Owen’s first hat-trick since he joined the Old Trafford side in the summer – and his first for anyone since 2005.