"For me, it's impossible to lose a match when I've only been broken one time", Zverev said.
And he underlined his status as the man to beat in Shanghai as he battered the Italian Fognini 6-3, 6-1.
Zverev has already joined Federer and Shanghai top seed Rafael Nadal in the field for next month's ATP Finals in London.
Federer will play Richard Gasquet in the quarterfinals.
Del Potro dropped his opening service game of the match as Zverev took the first set comfortably in just 26 minutes.
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.
A fan at least came away with a demolished racquet for a souvenir after the young German handed it to a spectator. "I just had to find my way through the whole match".
"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". On the basis of his victory over Zverev, nobody should rule out Del Potro's London credentials.
"I saw his frustration, for sure. But I think he's still very young and he needs to keep learning, as he's doing now", said the Argentine. Remember when Roger [Federer] was young?
American broke at love in the second game of the second set when Dimitrov sent a routine forehand into the net, although he didn't stay in front for too long.
In other third-round action, Spain's Albert Ramos Vinolas stopped German Jan-Lennard Struff 7-6 (7-4) 6-4.