Novak Djokovic dropped a set for the first time this week against the Greek world number five.
But the Serbian still extended his winning streak against Tsitsipas to eight matches with a 6-2 3-6 7-6 (4) victory.
"It's very sweet, obviously, when you win matches like this against one of the best players in the world," Djokovic said after the victory. "I thought I started the match very well, again, great hitting like yesterday in the quarters. I had chances early on in the second, I didn't break his serve. The momentum shifted, the crowd got into it. I think he elevated his level of tennis.
"Deservedly so, we went into - both of us - into an even battle all the way until the last point, until the last shot.
Some incredible points towards the end. I'm just really glad to overcome this challenge."
Djokovic will face unseeded Danish teenager Holger Rune, who was a surprisingly comfortable 6-4 6-2 winner against in-form Canadian eighth seed Felix Auger-Aliassime, in Sunday's final.
