Fritz is set to face either Jannik Sinner or Casper Ruud in the final on Sunday.
Alexander Zverev secured a spot in the last four of the ATP Finals on Friday with 7-6 (7/5), 6-4 victory over Carlos Alcaraz which leaves the Spaniard's destiny out of his hands.
World No. 3 Alcaraz beat Rublev 6-3, 7-6 (10/8) to lift himself off the bottom of the John Newcombe Group.
Alexander Zverev opened his campaign at the ATP Finals in Turin on Monday evening by dispatching Andrey Rublev 6-4, 6-4 in their round-robin opener.
Germany's Alexander Zverev won the Paris Masters on Sunday by defeating home hope Ugo Humbert 6-2, 6-2 in a dominant display by the new world number two.
Alexander Zverev beat fierce rival Stefanos Tsitsipas in the quarter-finals of the Paris Masters on Friday, while Holger Rune edged Alex de Minaur to keep alive his hopes of reaching the ATP Tour Finals.
Lorenzo Musetti stunned world number three Alexander Zverev to reach the semi-finals in Vienna on Friday, describing his comeback triumph as "a pretty big win".
Alexander Zverev and fellow Grand Slam veteran Grigor Dimitrov look to make the US Open semi-finals on Tuesday
Coco Gauff joined Novak Djokovic and Carlos Alcaraz on the US Open scrap-heap Sunday as the defending champion crashed out to Emma Navarro in a blizzard of mistakes.
Jannik Sinner ended his losing streak against Alexander Zverev with a 7-6 (11/9), 5-7, 7-6 (7/4) win on Sunday which took him into the final of the Cincinnati Open.