The seventh-seeded Tsitsipas earned his first win over a top 10 player this season, hitting 37 winners to 28 for Zverev.
The Greek took a 3-0 lead but failed to serve out the first set at 5-3 by sending a backhand into the net.
In the tiebreaker, Tsitsipas capitalized on two consecutive forehand errors from Zverev to lead 5-2 before taking the first set with an ace.
Tsitsipas broke Zverev in the opening game of the second set and clinched the victory with his 10th ace.
Zverev can still qualify for the ATP finals but now depends on the results of other players.
De Minaur, who got a walkover into the quarterfinals after the fourth-seeded Sinner withdrew, will next play the fifth-seeded Rublev, who ousted qualifier Botic Van de Zandschulp 6-3, 6-3.