He won on a third-set tie-break - his second in as many days - 7-6 (7-1) 3-6 7-6 (7-4).
Djokovic, coming off his fourth Wimbledon title last month, had seven aces and never faced a break point in the 1-hour, 25-minute match.
Tsitsipas, the world number 27, secured his place in his first Association of Tennis Professionals Masters 1000 quarter-final with a shock 6-3, 6-7, 6-3 win at the Aviva Centre.
"I'm happy to see Stan playing well again".
"I remained tough", Tsitsipas said. I had my chances to come back in the third set when I dropped my serve at 15-40.
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. Commenting on an eventual match against the Serb, Polansky said: 'His game style, he's a little bit better for me, let's say, compared to when I play (Roger) Federer second round just because Federer takes the ball so early and really puts a lot of pressure on you with that', admitted Polansky, who lost to Federer at last year's Rogers Cup. "I didn't play well". I don't know about giving two away in your home country, regardless to a top player.
Tsitsipas struggled with a first-serve percentage of 47 per cent, well below Zverev at 70 per cent. "People seemed to love it, loved the show and everything".
"He played very well and deserved to win without a doubt", Djokovic said.
Raven Klaasen of South Africa and Michael Venus of New Zealand beat Americans Mike Bryan and Jack Sock 7-6 (5), 6-4 while Croatia's Nikola Mektic and Austria's Alexander Peya defeated Anderson and Djokovic 7-5, 7-5.
Canadian teen Denis Shapovalov went down to Robin Haase, losing 7-5, 6-2, ending local interest.
Toronto's Daniel Nestor - the oldest player at the tournament at 45 - and Vancouver's Vasek Pospisil were scheduled to play their first-round doubles match in the late afternoon. Zverev beat Roger Federer in last year's singles final at Montreal.