He set up a semifinal with six-time champion Roger Federer by defeating John Isner 7-6 (5), 6-3 on Friday.
Zverev is the youngest player at 21 to reach the semifinals since 2009 and the first from Germany since 2003.
"The tournament isn't over," Zverev said. "I don't want to really be thinking 'I'm in the semifinals now, I'm satisfied.' That's not how I work."
Isner and Marin Cilic, who later lost 7-6 (7), 6-2 in a dead rubber against group winner Novak Djokovic, were eliminated by the result.
Five-time champion Djokovic will face debutant Kevin Anderson in the other semifinal on Saturday.
Isner needed to win in straight sets to have any chance of advancing and almost took the lead when he held a set point in the 12th game of the opener. Zverev saved it with an ace and played a faultless tiebreaker to eliminate the American.
"You make this tournament, you want to do a little bit better," said Isner, who lost all three of his matches. "But at the same time this is no normal event. You're up against the absolute best in the world."
In the second set, Zverev converted his only break point of the match to lead 5-3, before calmly closing out the contest at the O2 Arena.
Reaching the last four in London is the latest achievement in a career-best season for Zverev, whose victory over Isner took him beyond the 55 wins he posted last year.
Both players utilized powerful serves to hold comfortably but Isner came up with a crushing forehand return winner to bring up the first break point at 5-6.
Having forced a tiebreaker, Zverev produced perhaps the most important shot of the match to dig out a deep Isner return and force a volley error to ensure it was he and not the American who earned set point. "A remarkable shot," Isner said.
Isner netted a forehand and, with his chance of qualification gone, wilted in the second set as quality Zverev returns secured the only break of the match.
The 37-year-old Federer holds a 3-2 career record over Zverev, with the most recent meeting between the oldest and youngest player in the tournament having been a three-set victory for the Swiss at last year's ATP Finals.
"It's going to be a very difficult match," Zverev said. "I mean, him on this surface, indoor court, he's an unbelievable player."
The top-ranked Djokovic ensured he will be the only unbeaten semifinalist. Despite having already secured an eighth semifinal appearance with his previous victory, the Serb showed no signs of complacency as he lost just five points on his serve against Cilic.
Djokovic won 31 straight service points from the third game of the first set through to the fourth game of the second, but he did have to save a Cilic set point on his way to winning a closely fought tiebreaker.
"It wasn't easy to approach this match with 100 percent willingness to win it," Djokovic said.
Cilic, who has failed to advance from the round robin stage in four appearances, was unable to maintain his level of performance in the second set and allowed Djokovic to break twice.
Djokovic ended a two-year Grand Slam title drought by defeating Anderson in the Wimbledon final, before going on to claim his 14th major title at the U.S. Open.
"He's playing well, serving well, very aggressive," Djokovic said of Anderson. "So I know what to expect."