Tsitsipas saved 11 of 12 break points and took advantage of an error-filled performance from Federer — who continually put his opponent under pressure only to come up short when it mattered.
The top-ranked Spaniard still needs help from Daniil Medvedev to avoid an early exit.
Stefanos Tsitsipas began his campaign in style as he beat Daniil Medvedev in straight sets.
Djokovic, last year's runner-up, is bidding for the year-ending No. 1 ranking.
Roger Federer eased past Stefanos Tsitsipas 6-4, 6-4 in the Swiss Indoors semifinals.
The defending champion from Serbia, a four-time winner of the Shanghai Masters who had reached the semifinals in all eight of his appearances at the tournament, lost to sixth-seeded Stefanos Tsitsipas 3-6, 7-5, 6-3 on Friday in the quarterfinals.
The umpire told Stefanos Tsitsipas it was time to play, but Tsitsipas was still reaching into his bag for a new headband and screamed at Damien Dumusois that he still needed time to change.
Stan Wawrinka outlasted Greece's Stefanos Tsitsipas 7-6 (8-6), 5-7, 6-4, 3-6, 8-6 in a marathon French Open fourth-round clash that lasted five hours and nine minutes.
Rafael Nadal took his revenge on Tsitsipas he beat the Greek 6-3 6-4 to enter the final of the Italian Open.
Nadal's slump on clay continued on Saturday at the Madrid Open with a third consecutive semifinal elimination, adding to his worst start to the clay-court swing since 2015.
Roger Federer defeated Stefanos Tsitsipas 6-4, 6-4 in the final of the Dubai Championships on Saturday.
Federer's final hurdle in the tournament is Stefanos Tsitsipas of Greece who had shown him the door during the 2019 Australian Open.
Tsitsipas' run to the first major semifinal of his nascent career was most notable for the way he beat 20-time major champion Federer in the fourth round, saving 12 of 12 break points across four sets.
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