"I think I first qualified for this tournament in Shanghai in 2002 when I was 21, so I'm very excited for Alex - he has a very bright future ahead of him".
"It's been a tough group so to be through in two matches is great".
He may still have to beat Zverev in his final group match to qualify, with the talented German going up against favourite Roger Federer later on Tuesday.
Zverev earned a set point of his own at 6-5 but could not convert and Federer made his third set point count.
"I'n happy and relieved that I can play freely against (Marin) Cilic, instead of it being a nailbiter".
He hit a powerful forehand victor to let his intentions known early on and set up three break points in the opening game.
But Zverev went to pieces in the tie-break, only to fight back from 2-0 down in the second, capitalising on a noticeable Federer dip including five consecutive missed serves.
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The tension returned in the final game of the set, with Zverev facing multiple break points amid distractions from the crowd and celebrating a point he'd thought he'd won only to be overruled by Hawk Eye, but he got the hold nonetheless to force a breaker in the first.
Coming into the match Federer, 36, and Zverev had faced each other four times and each had won twice.
Jack Sock was woken at 4am by a fire alarm and had to leave his hotel, but he still found the strength to overcome Marin Cilic in a marathon ATP Finals round-robin match on Tuesday. "It's been an interesting morning, a fire alarm went off at 4am and we all had to exit our hotel so it was a long morning". My coach growing up nicknamed me "Showtime" because I love playing in front of people, and there is always a lot going on.
The Swiss star composed himself again to break down a man 16 years younger with six straight games in the third set to make it through to the semi-finals after two hours and 11 minutes of action. "It's an awesome atmosphere, you make me feel like home".
Nadal, who certainly enjoys playing on clay, had earlier vented his frustration about the hard-court surface at the ATP Finals and suggested that it would be better if the season-ending event at least occasionally took place on his preferred surface.
Novak Djokovic, Andy Murray and Stan Wawrinka are all long-term absentees from the Tour this season.