World number three Zverev, fresh off his maiden Grand Slam title at the French Open, lost 6-7(4), 6-4, 7-5 in a match lasting two hours and 39 minutes.
The 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.
He will face Germany’s Daniel Altmaier or fellow American Frances Tiafoe in Sunday’s title clash.