Tsitsipas set up match point with a scorching cross-court victor before completing the victory in 2 hours, 17 minutes.
Nadal is next scheduled to face Croatian Marin Cilic, who beat Argentina's Diego Schwartzman 6-3, 6-2.
"I kind of fooled him when I was on the court", Tsitsipas said. And I actually thought I was playing bad the whole match. Even his win over Serbia's Djokovic was not pulled out of a hat. "I just patiently waited for the moment and it happened". "I knew I was playing pretty good today".
Heavy morning rain pushed back the opening matches at the York University campus in the north end of the city by about an hour, holding off the start of an exciting day that featured six Canadian players, including Montreal's Felix Auger-Aliassime on his 18th birthday.
"Losing the second set, it was tough to deal with - I had my opportunities and didn't use them".
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"So, I can call it the best moment of my life".
Second seed Caroline Wozniacki of Denmark also crashed out after she lost 5-7, 6-2, 7-6 to Belarus' Aryna Sabalenka. 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.
He took advantage of a Djokovic unforced error for an early break at 4-2 and used a few 210-km/h serves to take the first set by holding at love.
Tsitsipas struggled with a first-serve percentage of 47 per cent, well below Zverev at 70 per cent. "I was fearless. I played exactly how I had to play at that moment".
Garcia proved too strong for Sharapova with a 6-3, 6-2 win and will take on top seed Simona Halep of Romania in the quarter-finals of the Women's Tennis Association Premier 5 tournament.
Tsitsipas will face second-seeded Alexander Zverev of Germany, the defending champion coming off a tournament victory last week in Washington that included a semifinal win over Tsitsipas.