The 21-year-old German moved ahead early in the second set but Tsitsipas broke at 3-5 and held serve to pull event.
Tsitsipas reached his first ATP World Tour final earlier this year at a clay-court event Barcelona, losing to Spanish great Rafael Nadal in the championship match.
Second-seeded Alexander Zverev of Germany, the victor last week in Washington, beat American Bradley Klahn 6-4, 6-4, and fourth-seeded Kevin Anderson of South Africa edged Russia's Evgeny Donskoy 4-6, 6-2, 7-6 (0).
He rounded off his afternoon with back-to-back winners to send Djokovic, the victor of 30 Masters titles, out on a first match point. "I feel like I'm playing well", Zverev said.
BC-TEN-Toronto, 5th Ld-Writethru, 512Greek teen Tsitsipas upsets Djokovic in TorontoAP Photo FNG105, FNG115, FNG116, FNG112, NSD124, NSD115, NSD117Eds: Updates with Nadal quote.
Why we lost to Manchester United - Leicester City coach, Claude Puel
The France World Cup victor did captain United on Friday and netted a penalty in the 2-1 victory over Leicester. The three promoted sides to the Premier League though have done a lot of business.
Grigor Dimitrov will face Anderson next after finding some of his best serving to beat Frances Tiafoe 7-6 (7/1) 3-6 7-6 (7/4).
The Greek teenager, who turns 20 on Sunday, followed up his defeat of seventh seed Dominic Thiem, beating four-time champion Djokovic, seeded ninth, in a first-time meeting. I had my chances to come back in the third set when I dropped my serve at 15-40. "I don't think he played well". But if he wins, it would be a match that I'm really looking forward to'. "I just patiently waited for the moment and it happened".
The tennis player further credited Tsitsipas for the victory and praised him for displaying commitment and discipline on the court.
The rain, which started up again with a fury after Djokovic's one-hour, 25-minute win, also caused a venue switch from centre court to the grand stand for Canadian Denis Shapovalov's late afternoon match against 14th-seed Fabio Fognini. "We want to see young players playing well and challenging the best players in the world".
In the doubles quarterfinals, the top-seeded duo of Austria's Oliver Marach and Croatia's Mate Pavic edged Jean-Julien Rojer of the Netherlands and Romania's Horia Tecau 6-7 (5), 7-5, 10-6.