Top seed Rafa Nadal battled past Swiss wild card Stan Wawrinka 7-5 7-6(4) and will next meet Marin Cilic, who took down Argentinian Diego Schwartzman 6-3 6-2.
A confident Tsitsipas sent a blistering forehand to the back corner while the ninth-seeded Serbian was heading the other way on his first match point to secure the win before looking at his box in disbelief.
"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 in an on-court interview. "I never expected to beat such a top-ranked player and such a high-respected player like Novak."
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.
The Greek teen made some errors near the end of the second set that allowed Djokovic, a four-time winner of the tournament, to set up a decider.
However, Tsitsipas did well to break Djokovic for a 2-0 lead in the third set and never looked back.
For the resident of Athens, who arrived in Toronto fresh off a run to the semi-finals in Washington where he lost to German world number three Alexander Zverev, the win is the latest in a breakthrough campaign during which he has reached the quarter-finals or better at seven ATP main tour events.
Tsitsipas, who beat Austrian seventh seed Dominic Thiem in the second round here, will next face Zverev after the second seed beat Russian qualifier Daniil Medvedev 6-3 6-2.
In other matches, fourth seed South Kevin Anderson beat Belarusian qualifier Ilya Ivashka 7-5 6-3 and fifth seed Grigor Dimitrov advanced with a 7-6(1) 3-6 7-6(4) win over American Frances Tiafoe.
Russian Karen Khachanov eliminated American John Isner 7-6(5) 7-6(1) in match that featured no service breaks.
(Editing by Pritha Sarkar/Peter Rutherford)
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