The 27-year-old Briton kept his cool in the final that was suspended after only 23 minutes on Sunday, winning the title in his maiden claycourt final appearance as he prepares for the French Open starting later this month.
The players resumed with local favourite Kohlschreiber leading 3-2 in the first set and they both confidently held serve to go into the tiebreak.
Fired on by new coach Jonas Bjorkman in the stands, world number three Murray got the mini break he needed and snatched the set after almost an hour.
Murray, leading 4-3 in the second set, had a golden opportunity to break Kohlschreiber with three break points but the German held his nerve and his serve to clinch the set to level the contest.
The pair traded blows in the third with both holding on to force another tiebreak.
Murray clinched victory on his second match point when Kohlschreiber, winner in Munich in 2007 and 2012, sent a backhand long.

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