Rafael Nadal won his 14th consecutive match to reach the Shanghai Masters quarterfinals, beating Fabio Fognini of Italy 6-3, 6-1 on Thursday.
But Del Potro levelled by taking the second set on a tie-brack, and when the 29-year-old secured a break of serve in the decider the red midst descended on Zverev.
Zverev came to the match strong and raced to a 3-0 lead in the first set within 10 minutes.
Dimitrov, chasing a spot at the season-ending ATP Finals in London, beat American Sam Querrey 6-3, 7-6 (3) to set up a Chinese reunion with Nadal. "I'm a bit pissed off because I feel like I played well and that's the upsetting part of it - I could have done great in this tournament".
Federer will play Richard Gasquet in the quarterfinals.
CM Arvind Kejriwal's auto stolen from Delhi Secretariat
The vehicle was donated to Kejriwal by Kundan Sharma, a software engineer, in January 2013. An FIR has been registered in connection with the incident.
Zverev, 20, has already qualified for the ATP World Tour Finals at the O2 next month but is yet to decide if he will play in the NextGen Finals in Milan, the new ATP tournament featuring the world's top 21-and-under singles players across the ATP World Tour season.
Alexander Zverev faces Juan Martin del Potro in Round of 16.
Zverev all but handed the match to del Potro when he dropped a crucial service game midway through the fifth set, hitting a cross-court backhand into the net.
Del Potro knew Zverev's reaction to losing serve was likely a good omen. "And that's what I did for the second and the third set", the 2009 US Open champion Del Potro said. "He's still very young and has to keep learning".
6-4 in one hour and 55 minutes to set up a quarter-final meeting with John Isner or Viktor Troicki.