The American eased to a 6-3, 7-6(0) victory despite being held up by a lengthy rain delay early in the second set.
Fritz has now won his last five meetings with Zverev and is set to climb to fourth in the world rankings, a place behind the German.
"I'm really happy especially as it was not too great of a clay season. And then from that place to come here and start the grass season off perfectly, I am super happy to win the title and do it here," said Fritz, who won the ATP 250 title without dropping serve all tournament.
"I don't have much time to celebrate. I have doubles tomorrow in London, in Queen's."
Last year's US Open runner-up lifted his first trophy since winning in Eastbourne 12 months ago, also on grass.
"I've had enough, stay away from me. Please don't come to Germany for the next two or three years," Zverev said, having lost his third final on grass after losses to Roger Federer in Halle 2017 and fellow German Florian Mayer in Halle 2016.
Fritz moved into a one-set lead courtesy of a break in the eighth game.
He missed the only break point of the second set but raced through the tie-break, winning the last 11 points of the match.