Nadal will face Stan Wawrinka in the round of 16 after the Swiss rallied to beat Hungarian Marton Fucsovics 1-6 7-6 (2) 7-6 (10).
The big-serving sixth-ranked South African hit 15 aces and won 86 per cent of first serves in en route to the 7-5 6-3 victory.
With this, he reached his maiden ATP World Tour Masters 1000 quarter-final. 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.
'That break [in the third set] was everything.
Tsitsipas, who beat seventh-seeded Dominic Thiem and ninth-seeded Novak Djokovic earlier in the week, became the youngest player to beat three top-10 players at one tournament since Rafael Nadal - who was also 19 - did it at Monte Carlo in 2006.
In other results, fourth seed and Wimbledon runner-up Kevin Anderson downed Ilya Ivashka of Belarus in straight sets.
"I thought Tsitsipas played very well and he deserved to win without a doubt", Djokovic said.
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At 30-40, Zverev floated his second serve well long to end the match in two hours 27 minutes. But as I said, I didn't feel the ball at all.
"Yeah, well, I mean, I must admit it was exciting, but it was also unusual because, you know, he's a top player", he said.
"I was really not focusing on winning or losing, just on starting to play good tennis and start building the right habits".
"The level of tennis today, in my opinion, was not the highest - it was alright", Tsitsipas said.
Milos Raonic of Thornhill, Ont., was scheduled to follow Djokovic's win on centre court but that match was also delayed.
Tsitsipas, who turns 20 on Sunday, relied on his serve and forehand combination to get by Djokovic, who was competing in his first tournament since collecting his 13th grand slam title at the All England Club last month. Khachanov beat eighth-seeded John Isner of the United States 7-6 (5), 7-6 (1), and Haase topped Canadian Denis Shapovalov 7-5, 6-2. Zverev beat Roger Federer in last year's singles final at Montreal.