Tsitsipas, the 19-year-old rising star, took two hours and 17 minutes to beat Djokovic in his first-ever match against the ninth-seeded Serbian, a victor of four Canadian Open titles and a 13-time Grand Slam champion.
Tsitsipas now faces defending champion Alexander Zverev in the final eight after the German routed Daniil Medvedev in straight sets.
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 knew I was playing pretty good today".
Tsitsipas showed his nerve right from the start, as he surprised Djokovic (and everyone else watching) with a 5-2 game lead.
Tsitipas, who turns 20 on Sunday, beat the 13-time Grand Slam champion 6-3 6-7 (5-7) 6-3 in two hours 18 minutes. "I'm putting Greece more deep into the map of tennis", Tsitsipas said. "I would say I played OK". He just played better in the decisive moments.
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Kevin Anderson beat Ilya Ivashka 7-5 6-3 but his Wimbledon semi-final opponent John Isner didn't fare as well, losing 7-6 (7/5) 7-6 (7/0) to Karen Khachanov.
He held serve to open the set and wrong-footed Djokovic after the veteran served at deuce, setting up an overhead smash for the advantage before a brilliant backhand victor secured a 2-0 lead.
Djokovic had a quick break before returning to the doubles court with Anderson.
Tsitsipas was ranked 168th in the world a year ago but has since rocketed to No. 27.
Tsitsipas, who beat seventh-seeded Dominic Thiem and ninth-seeded Novak Djokovic earlier in the week, became the youngest player to beat three top-10 players at one tournament since Rafael Nadal - who was also 19 - did it at Monte Carlo in 2006.
The tennis player further credited Tsitsipas for the victory and praised him for displaying commitment and discipline on the court. Haase instead played Mikhail Youzhny, beating the Russian 7-5, 6-2. Nadal opens his 2018 Rogers Cup campaign in Toronto on Wednesday.