The new British number one had lost his previous two finals but made it third time lucky with a brilliant three-set win over former Wimbledon runner-up Matteo Berrettini.
Draper showed he has a game for the big stage with a 3-6 7-6 (5) 6-4 win against an opponent who was gunning for a third title in the German city.
Victory for Draper moves him up to a career high ranking of 31, which would be good enough to be seeded at Wimbledon.
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