Zverev, fresh from his Roland Garros triumph that ended his long wait for a grand slam crown, converted his second match point on Friday after almost exactly two hours to take his winning run to 10 matches over the clay and grass
In front of a well-filled centre court, the top seed and the qualifier played out a hard-fought match, with both big servers sending down 14 aces.
"It was an incredible match, a high level from both players," Zverev said. "It could also have gone two sets the other way."
Zverev has made the semi-finals at the Wimbledon warm-up for the fourth consecutive time but he's never won at the western German event.
His next opponent Taylor Fritz earlier got a revenge of sorts when he saved a match point to beat fellow US star Ben Shelton in a dramatic quarter-final.
Fritz won six days after losing the Stuttgart final against left-hander Shelton. He'd also lost the Dallas final in February against the same opponent.
This time, Fritz prevailed 6-7 (7-5) 7-6 (10-8) 7-6 (7-3) in a really tight affair over two hours 49 minutes in sweltering conditions, saving his match point at 7-6 in the second set tie-break.
Fritz fired 24 aces and saved four break points, while Shelton faced no break points and had 15 aces.
"I don't know if I could have taken losing another one of those to Ben," Fritz said.
"When I say that, I mean just doing everything but winning the match, because the funny thing about this one is he had the chances. In the other two he won, I probably had the better chances."
Fourth seed Daniil Medvedev was beaten by German journeyman Daniel Altmaier in the third quarter-final, much to the joy of the Halle crowd.
Altmaier outlasted the Russian 6-4 6-7 (8-6) 6-4 for a famous home victory.
He plays Frances Tiafoe in Saturday's last four as the prospect of an-all German final ramps up.
US hope Tiafoe beat second seed Felix Auger-Alliasime 3-6 6-3 7-6 (14-12) after a mammoth tie-break.
Wimbledon starts a week on Monday.
