Russia's Rublev joins Djokovic in Turin ATP Finals semis
Rublev's win saw him overtake Tsitsipas in the Red Group to take second place behind Novak Djokovic.
With the group stage now over Djokovic faces the American Taylor Fritz with Norway's Green Group winner Casper Ruud awaiting Rublev in Saturday's semis.
In a winner-takes-all encounter with the last place in the semi-finals at stake Tsitsipas looked set to win a third head-to-head with Rublev this season with a powerful first set.
But the world ranked number seven Rublev showed no nerves in the big moments thereafter and overpowered the Greek with the quality of his ground strokes, earning his first ATP finals semi-final encounter.
"I didn't give up. I kept fighting and playing," Rublev said. "I just gave my best and I managed to turn the match around and I am happy to be in the semis."
Djokovic marked himself out as the favourite when he remained unbeaten earlier Friday producing a battling 6-3, 6-7 (5/7) 7-6 (7/2) win over Daniil Medvedev.
The 21-time Grand Slam winner Djokovic had gone into the dead rubber already assured of his place in the semis after wins over both Rublev and Tsitsipas.
While Medvedev in contrast was already eliminated after losses in both his outings on the hardcourt in Turin.
After having to dig deep into his mental and physical reserves Djokovic said: "Daniil and I have had some battles in the past and I knew coming into the match that it was going to be his last match of the season and he wouldn't want to finish with a loss.
With both players trading punches like heavyweights in the ring Djokovic took the first set only for Medvedev to force a decider sealing the second set on his fourth set point.
Djokovic rallied back from a break down to earn his 40th tour-level win of the season after three hours and five minutes.
"He was playing really quick. I didn't feel physically well in the third set, struggled a lot. It is a battle and it is a fight," he said.
"But I think the biggest battle, as I've said before, is always the inner battle. If you manage to find yourself in that optimal state of mind and body as often as you possibly can, I feel you can extract the best and reap the best results for yourself in every moment, every point, every match," he explained.
The 35-year-old is aiming to tie Roger Federer’s record six triumphs at the tournament, which is being held in Turin for the second time.
The former World No. 1 has now won 16 of his past 17 matches, having triumphed in Tel Aviv and Astana last month.
Aside from his three on court wins this week, he was boosted by the news that he has been granted a visa to play in the Australian Open in January.
He was kicked out of the country in the lead-up to the Melbourne Grand Slam earlier this year after refusing to be vaccinated against Covid-19.