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The fresh-faced 21-year-old from Hamburg, who is coached by his father, beat Argentina's Guido Pella in the 2017 final.
Kohlschreiber, a triple champion in Munich, had not lost a single set coming through the rounds.
But the 34-year-old had two break points in the sixth game of the first set only to lose the game and then get broken in the next game.
Zverev, the great hope of German tennis, then broke his older compatriot in the opening game of the second set and never looked back.