Nadal and Federer were both due on court later, with the Spanish top seed playing Fabio Fognini of Italy and second seed Federer facing Alexandr Dolgopolov. You save a little bit more the body.
Del Potro, who won the US Open eight years ago over Roger Federer but has struggled for a long time with multiple wrist surgeries and recovery, lost the 2013 Shanghai final to Novak Djokovic in his best performance at the event.
Nadal, enjoying a late-career flourish, defeated good friend Dimitrov on his way to winning the China Open on Sunday, his sixth title of the season.
Federer will play Richard Gasquet in the quarterfinals.
The victor of that match may well meet Roger Federer in the semi-finals - a man whom Del Potro downed at the US Open.
Del Potro dropped his opening service game of the match as Zverev took the first set comfortably in just 26 minutes. He repeatedly smashed his racket until it was a mangled mess.
"Those are the matches I really want to win", Dimitrov said. "I just had to find my way through the whole match".
Zverev was hoping to secure a place in the quarter-finals of the big tournament in China against Argentine veteran Del Potro.
"I saw his frustration, for sure", del Potro said. "He has everything to be in the top of the game".
A fan at least came away with a demolished piece of memorabilia after the young German handed it to a spectator while Del Potro ran away with the match to complete a 3-6 7-6 (7-5) 6-4 victory.
Fourth-seeded Marin Cilic will face Albert Ramos-Vinolas of Spain.