Tsitsipas set up match point with a scorching crosscourt victor before completing the victory in two hours 17 minutes. "So just all in all, it wasn't that great of a match". A former world No. 1, Djokovic is seeded ninth in the event he last won in 2016.
When the weather passed, the pair returned, with Nadal wrapping up the set on his second chance.
Both players secured early breaks in the deciding set and Tsitsipas - who had started to mix up his shots more often and change service speeds - saved three break points to pull ahead 5-4.
He won on a third-set tie-break - his second in as many days - 7-6 (7-1) 3-6 7-6 (7-4).
But Tetipas made a good offer to break Jukovic's lead and lead 2-0 in the third set and did not back down.More news: Alisson set for debut against West Ham United
"He played very well and deserved to win without a doubt", Djokovic said.
"I'm going to get into Cincinnati, the only [Masters] 1000 event that I didn't win in my career, and hopefully I can have a good tournament", ATP website quoted Djokovic, as saying.
Second seed Caroline Wozniacki of Denmark also crashed out after she lost 5-7, 6-2, 7-6 to Belarus' Aryna Sabalenka.
Also, Karen Khachanov of Russian Federation beat 12th-seeded Pablo Carreno Busta of Spain 6-4, 7-6 (3); Ilya Ivashka of Belarus topped American Ryan Harrison 7-6 (5), 6-4; and American Frances Tiafoe edged Canada's Milos Raonic 7-6 (4), 4-6, 6-1.
Djokovic, a 13-time Grand Slam champion, couldn't claw back and eventually seemed resigned to the result, even smiling a few times in the final game. 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. "I didn't crack under pressure. In the moments when I probably needed to step it up, I did".More news: Local pilot reacts to stolen Horizon airplane
Tsitsipas raised his arms and tossed his racket in the air after sealing the win.
In Friday's quarter-finals in Toronto, he will take on 21-year-old German No. 2 seed Alexander Zverev, who defeated Russia's Daniil Medvedev 6-3, 6-2 on Thursday. They beat French duo Pierre-Hugues Herbert and Nicolas Mahut 4-6, 6-4, 10-7.
But now, Tsitsipas has entered his seventh ATP World Tour quarter-final of the season.
The 19-year-old who has been on fire also reached the fourth of the Wimbledon championships this year only to lose to American John Isner.
Play continues through Sunday at the US$5.94-million tournament on the York University campus.More news: Omarosa in new book: I saw Trump’s racism ‘with my own eyes’
The tennis player further credited Tsitsipas for the victory and praised him for displaying commitment and discipline on the court. Nadal opens his 2018 Rogers Cup campaign in Toronto on Wednesday.