Bulgarian fifth seed Grigor Dimitrov required nearly two and a half hours to subdue Frances Tiafoe of the United States 7-6 (7/1), 3-6, 7-6 (7/4).
The ninth-seeded Serb, competing in his first tournament since his Wimbledon triumph last month, won a dominant 83 percent of his first service points and wrapped up the day's opening match minutes before the first of several rain delays.
The 21-year-old German moved ahead early in the second set but Tsitsipas broke at 3-5 and held serve to pull event.
Tsitsipas, ranked 27, spent just over two hours in advancing to the first Masters 1000 quarter-final of his career. "I think before he was playing really bad". But even the Andy one, I was a little surprised by that one just because he was entered on his protected ranking, and the Federation chose to help him out so he could pull out with his protected and get a wildcard entry so he could save it for another tournament.
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In the third set, the teenager showed great composure to break for a 2-0 lead and then saved a break point for a 3-0 margin. (The early break in the third set) was everything.
Anderson topped qualifier Ilya Ivashka of Belarus 7-5, 6-3, and Dimitrov beat American Frances Tiafoe 7-6 (1), 3-6, 7-6 (4).
"It's a dream of any kid out there in this world, any kid that's playing tennis, to beat these kinds of players, so I can call it the best moment of my life", a shocked Tsitsipas said on Thursday.
Heavy morning rain delayed the match by about an hour.
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The tennis player further credited Tsitsipas for the victory and praised him for displaying commitment and discipline on the court. But as I said, I didn't feel the ball at all. He just played better in the decisive moments.
Tsitsipas struggled with a first-serve percentage of 47 per cent, well below Zverev at 70 per cent. It was a very emotional win. Tsitsipas lost to Zverev last week in Washington, D.C.in the semifinal.
Raven Klaasen of South Africa and Michael Venus of New Zealand beat Americans Mike Bryan and Jack Sock 7-6 (5), 6-4 while Croatia's Nikola Mektic and Austria's Alexander Peya defeated Anderson and Djokovic 7-5, 7-5.
Veteran Dutchman Robin Haase advanced to the quarter-finals for the second consecutive year, beating Denis Shapovalov 7-5 6-2.
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