The world number 27 is through to the first ATP World Tour Masters 1000 quarter-final of his career.
"Losing in this kind of tournament, it's not something I don't care about", Djokovic said.
The favourite was much improved in the second set but still could not shake off Tsitsipas, needing to save two late break points as his opponent closed on victory.
Speaking after his Rogers Cup exit, Djokovic said: 'I just played not that great, especially from the baseline.
Tsitsipas, who turns 20 on Sunday, relied on his serve and forehand combination to get by Djokovic.More news: Liverpool too strong for new-look Hammers
"I was waiting and I grabbed him like a bulldog and I stuck there", Tsitsipas said.
However, Tsitsipas did well to break Djokovic for a 2-0 lead in the third set and never looked back.
World number one Rafael Nadal is also through to the last eight. "With each game, with each point that I play, I feel more confident, more stable on the court, and everything falls into its place". "Just happy to be in the quarterfinals".
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).
Alexander Zverev only needed two sets to knock out Daniil Medvedev, winning 6-3, 6-2.More news: Arsenal manager Unai Emery insists all is Wel-beck with Danny
"So I'm pretty used to that".
"I tried few things that I didn't try before, and I played a little bit more with variety and changed the pace a bit of the ball, played deeper, played smarter". 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.
Garcia proved too strong for Sharapova with a 6-3, 6-2 win and will take on top seed Simona Halep of Romania in the quarter-finals of the Women's Tennis Association Premier 5 tournament.
Earlier, fifth-seeded Bulgarian Grigor Dimitrov outlasted American Frances Tiafoe 7-6 (1), 3-6, 7-6 (4) and fourth-seeded South African Kevin Anderson topped qualifier Ilya Ivashka of Belarus 7-5, 6-3. Russian Karen Khachanov eliminated American John Isner 7-6 (7-5), 7-6 (7-1) in match that featured no service breaks.
Del Potro, who had a bye in the first round after reaching the Los Cabos final last week, was set to play Robin Haase of the Netherlands.More news: Mayfield to play 2 quarters in preseason opener