A former World No. 1, Djokovic is seeded ninth at the Toronto tournament.
In the tiebreaker, Zverev won a 20-shot rally to get his first match point at 6-5 but Tsitsipas poured on the pressure from the baseline and tied it. Tsitsipas saved another match point before converting his fifth set point at 13-11 when Zverev sprayed a return wide.
"It's a dream of any kid out there in this world, any kid that's playing tennis, to beat these kinds of players", Tsitsipas said. "To be on the same side of the net was great, and I enjoyed it very much so".
Milos Raonic of Thornhill, Ont., was scheduled to follow Djokovic's win on centre court but that match was also delayed. Maybe if I played Chung it could be a little bit just having the home crowd support.
He next faces Wimbledon runner-up and fourth seed Kevin Anderson who defeated Ilya Ivashka of Belarus 7-5, 6-3 to also make the last-eight. But if he wins, it would be a match that I'm really looking forward to'.
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It was the sixth time that Anderson has produced a five wicket haul at Lord's and he now has 99 Test wickets at the famous London venue.
"It was a good match, a very positive victory for me over a tough opponent", Nadal said. Italy's Fabio Fognini, the No. 14 seed coming off a victory at Los Cabos, fell out with a 6-3, 7-5 (14) loss to Canada's Denis Shapovalov. (The early break in the third set) was everything.
Tsitsipas let a double-break point opportunity slip at 4-4 in the second set, eventually giving up the game after back-to-back shanks. 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 made a decision 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.
"I was serving well so that break was everything", Tsitsipas said. "I was courageous. I played exactly how I had to play at that moment". But I think one is good to give away to a top player, but two is, in my opinion, pushing it'.
Tsitsipas will now move on to the quarter-finals of the "Rogers Cup" to fave Alexander Sverev, who recently knocked him out of the "Washington Open" semis.
Play continues through Sunday at the US$5.94-million tournament on the York University campus.