Friday night's concluding match of the Red Group was a straight shoot-out for the last available semi-final spot, after Novak Djokovic had secured his place in the last four with victory over Daniil Medvedev earlier in the day.
At first, it looked as if Tsitsipas was going to advance, after the Greek star seized the initiative with a dominant showing in the first set.
A crushing forehand winner handed him the decisive break in the fourth game, before Rublev tamely surrendered the set on a double fault.
But Rublev was able to cut down on his error rate significantly to produce a much better performance in the second set, and had the whole crowd in Turin behind him when he broke Tsitsipas for a 5-3 lead.
Tsitsipas had a chance to break back immediately after, but Rublev came up clutch to save the point against him before holding on to close out the set and level the scores.
The momentum was with Rublev now, and he would go on to boss the deciding third set, breaking for a 2-1 lead and again for 5-2 when a disintegrating Tsitsipas delivered back-to-back double faults.
The win sees Rublev reach the finals of the ATP Tour's season-ending showpiece for the first time in his career, where he will take on Norway's Casper Ruud.
"I just kept telling myself to keep fighting, keep playing, and we'll see what happens," Rublev said.
"I was happy that I was mentally strong today and I was able to turn the match around because Stef in the beginning was hitting super hard, hitting so many forehand winners."