The third-ranked German, a finalist at Halle in 2016 and 2017, entered the match with a poor recent record against Fritz, having lost his previous six meetings with the American.
He made a strong start, securing an early break, but Fritz responded to force a tiebreak, which Zverev won.
Fritz hit back in the second set, turning the momentum decisively in his favour by winning 12 consecutive points and levelling the match.
In the decider, both players were locked in a tense battle before Fritz produced a late break to seal victory and book his place in the final.
The 28-year-old struck 19 aces and won 87% of his first-serve points to snap Zverev’s 10-match winning streak.
"I felt like I played a good tiebreak (in the first set) and I felt I got a little unlucky with some bounce and he played some really good points and took one on my serve, and that was it," Fritz said.
"I felt like he was struggling with something. I am not sure what it was. I felt like I felt better than he did, so that was what I needed to tell myself to go to work."
Tiafoe dispatched Germany’s Altmaier with ease, breezing through the opening set before sealing a 6-1, 6-3 victory.