Tsitsipas dispatched Dominic Thiem, Novak Djokovic and Alexander Zverev in the previous three rounds before battling back to send the Wimbledon runner-up packing on a sun-soaked day in Toronto.
"It never gets easier. You just get better," Tsitsipas wrote on a camera lens after the match.
Tsitsipas will play his first ATP Masters 1000 final on his 20th birthday on Sunday against world number one Nadal after the Spaniard defeated Karen Khachanov 7-6(3) 6-4 in their rain-delayed evening match.
Fourth seed Anderson was unable to break Tsitsipas' serve on any of his four opportunities and saw his lone match point opportunity vanish when Tsitsipas smoked a backhand crosscourt winner in the third set tiebreak.
Tsitsipas, who stood well back of the baseline when receiving the South African's blistering serves, managed the only service break of the game in the third game of the second set with an overhead smash.
With the win, Tsitsipas is projected to climb to at least number 15 when the new rankings are released on Monday.
"I didn't even have this in my head," Tsitsipas said of reaching the final.
"I thought winning a couple of rounds would be amazing but I'm in the final already. I can't believe what just happened.
"I didn't aim that high and I think with low expectations I managed to pull out my best tennis."
Despite his recent success Tsitsipas will be a big underdog when he takes on French Open champion Nadal, who will be seeking his 33rd career Masters 1000 title.
Nadal overcame six aces from the big-serving Russian Khachanov to punch his ticket to his fifth final of the year.
"I'm happy with the way that I played and overall I think I have been improving," said the 32-year-old Nadal.
"Tomorrow is a big test against a player who is playing great, a young one.
"I am looking forward to play that match. I'm excited about it and it's an opportunity for me to play a good match against one of the best players."
Nadal dominated in his only previous meeting with Tsitsipas, a straight sets win in the final of the Barcelona Open on the Spaniard's preferred surface of clay.
(Reporting by Rory Carroll, editing by Pritha Sarkar and Sudipto Ganguly)
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