Zverev's victory means world number one Rafael Nadal failed to reach the last four despite coming from behind to defeat Greek hopeful Stefanos Tsisipas earlier on Friday.
Zverev, 22, outpassed Nadal in style in the opener, but lost to an on-fire Tsisipas in the second round. "For me, this was a must-win situation," said Zverev, who broke in the first game and has never given his opponent any break point on Friday evening, Xinhua news agency reports.
Zverev is going to meet Dominic Thiem on Saturday evening, who became the Group Bjorn Borg winner after defeating both Roger Federer and Novak Djokovic, even though the Austrian was beaten by Italian debutant Matteo Berrettini in his last group match.
"I've still got to improve. We're in the semifinals now and it doesn't get any easier from here. I'm going to have to play my best tennis to have a chance," said Zverev.
Earlier, Nadal took two hours and 52 minutes to outpass Tsisipas 6-7 (4), 6-4 and 7-5, winning two group matches both with sensational comebacks.
The Spaniard was awarded his year-ending world number one trophy after the victory. He has secured the top ranking after Federer ousted world number two Djokovic on Thursday.
"I am super happy," said Nadal, who spent nearly five minutes to thank his family, team and supporters. "Honestly, after all the things that I went through in my career, in terms of injury, I never thought that at the age of 33 and a half, I would have this trophy in my hands again. So it's something really, really emotional for me."
Tsisipas will fight for a final place against six-time champion Federer on Saturday. The 21-year-old debutant is the youngest in the squad while the 38-year-old Swiss legend is the eldest in the top eight.
( With inputs from IANS )