It was the 32nd title of the Scot’s career as he prepares for the French Open at the end of the month.
In a rain-interrupted match, the top-seed needed just over three hours to beat his world-ranked 24 opponent, who fought hard in front of his home crowd.
The pair could meet again in the second round of this week’s Madrid Masters.
The final resumed on Monday after heavy rain stopped play on Sunday evening with Kohlschreiber leading 3-2 in the first set.
Both players confidently held serve to take the opener into a tie-break, and it was world number three Murray, fired on by new coach Jonas Bjorkman, who got the mini-break to snatch the set after almost an hour.
Murray had three break points at 4-3 up in the second set, but Kohlschreiber held his nerve then broke Murray in the 11th game before serving out to level the match.
There were no breaks in the third set and Murray clinched tie-break victory on his second match point when Kohlschreiber, winner in Munich in 2007 and 2012, sent a back-hand long.