The 17th-ranked Bulgarian edged a high-quality encounter 6-3, 6-7 (1/7), 7-6 (7/3) to advance to his second Masters 1000 final - after winning the title in Cincinnati six years ago.
It was just Dimitrov's second win in eight meetings with Tsitsipas, who had yet to lose a set in making the last four at Bercy for the second year running.
"There were no tears but I got very emotional," said Dimitrov. "I am just living in the moment right now. It has been a funny road of late, but each win means more and more to me."
Dimitrov broke Tsitsipas in the Greek's opening service game and rolled into a 4-1 lead. Tsitsipas resisted two set points in the eighth game but Dimitrov wrapped up it with a routine hold.
Tsitsipas found himself on the ropes when Dimitrov brought up two break points at 4-all in the second set, but the seventh seed wriggled out of trouble and it went to a tie-break.
The Greek dominated from the outset and reeled off six straight points to steer the momentum back in his favour, taking the match to a deciding set.
Dimitrov faced his first break points in the third game of the decider, saving all four to put a spring back in his step and stall his rival's momentum.
The players exchanged a series of comfortable holds to set up another tie-break, this time Dimitrov seizing command by racing into a 5-0 lead before getting over the line with a crosscourt backhand.
"The first five points in the tie-break were excellent," said Dimitrov.
"I took those chances and that was all I could do against such a high-quality player. If you let him dictate you are done. But I kept on believing and kept staying focused and made sure every time I had the ball on the racquet I did something with it."
Dimitrov will face six-time champion Novak Djokovic or Andrey Rublev in Sunday's final.
In the last few weeks, Dimitrov has reached the semi-final in Chengdu, a quarter-final in Beijing and the semi-finals of the Masters 1000 event in Shanghai.
His path to the last four of the Paris indoor event included a shock defeat of world number three Daniil Medvedev in the second round, avenging his loss to the Russian last week in Vienna.
Dimitrov, who lost to Djokovic in the semi-finals in Paris in 2019, won his only Masters title in Cincinnati in 2017 - the same year he won the season-ending ATP Finals.
