The American eased to a 6-3, 7-6 (7/0) 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.
Last year’s US Open runner-up lifted his first trophy since winning in Eastbourne 12 months ago, also on grass.
Top seed Zverev is still waiting to win the first grass-court title of his career and he has never even reached the quarter-finals of Wimbledon, which gets under way on June 30.
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. (AFP)