US Open runner-up Medvedev, chasing his fourth ATP Tour title in a breakthrough 2019 season, will meet Germany's Alexander Zverev in Sunday's final.
Tsitsipas had never won a set in his previous three meetings against claycourt specialist and 11-times French Open champion Nadal, but the Greek drew first blood by saving a break point to hold in the 10th game and take the first set.
Rafael Nadal showed no signs of rust as he raced into a 5-0 lead against fellow Spaniard Roberto Bautista Agut in the first set on Court Rainier III, defending his Monte Carlo Masters title with 6-1, 6-1.
Swiss player Roger Federer overcomes Stefanos Tsitsipas 6-4 6-4 in Dubai final.
Roger Federer was challenged by Fernando Verdasco before defeating the Spanish veteran 6-3 3-6 6-3, reaching the quarter-finals of the Dubai Duty Free Tennis Championships.
"For the first time I play as if I was at home," said 20-year-old Tsitsipas, who reached the semi-finals at the Australian Open last month.
Nadal's win put him into his fifth Australian Open final and will face either top-seeded Novak Djokovic or Lucas Pouille at the final.
Tsitsipas, who was contesting the Masters 1000 final on his 20th birthday after four consecutive wins over top-10 players in Toronto, threw all he had at Nadal but was ultimately unable to beat the world number one.
As the Spaniard overcame Marin Cilic it was the Greek teen Stefanos Tsitsipas who was the talking point after he defeated defending champion Alexander Zverev in three sets.
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