Facing Francisco Cerundolo in the second round at the indoor tournament, Rublev lost 7-6 (8-6) 7-6 (7-5) after a match that lasted more than two hours on Tuesday.
Rublev was so frustrated at one point in the second set that he smashed his racket against his left knee at least seven times in succession. Video footage showed the outburst left his knee bleeding.
The Russian player held the eighth and final qualifying place in the race for the season-ending ATP Finals but could be overtaken by rivals, including Australia's Alex de Minaur, this week.
The ATP said that Taylor Fritz became the fifth player to qualify on Tuesday, making it to the season-ending tournament for the second time in the past three years.
The indoor event gathering the top eight players of the season will take place in Turin, Italy, from November 10-17.
Fritz joins Jannik Sinner, Carlos Alcaraz, Alexander Zverev and Daniil Medvedev in the field.
Earlier on Tuesday, big-serving Giovanni Mpetshi Perricard of France hit 28 aces on his way to defeating Frances Tiafoe 6-7 (7-5) 7-6 (7-4) 6-3.
Fresh from winning the title in Basel, Mpetshi Perricard also had 13 double-faults but never dropped his serve against the 14th-seeded American player.
Mpetshi Perricard converted his sole break point to win his first match at a Masters 1000 tournament.
The Frenchman, who started the year ranked 200th, rose to a career-high ranking of No.31 on Monday.
According to ATP statistics, Mpetshi Perricard has served 512 aces in just 27 matches this season. He will play Karen Khachanov, who overcame Australia's Christopher O'Connell 6-4 3-6 7-6 (8-6) in the second round.
There were better fortunes for another Australian, Alexie Popyrin, who downed Mario Berrettini 7-5 7-6 (7-2) and now faces Daniil Medvedev, the No4 seed.
On a good day for local players, Arthur Fils also progressed to the second round by edging Croatian Marin Cilic 7-6 (7-5) 6-4. He now meets Jan-Lennard Struff, who defeated Lorenzo Musetti 6-4 6-2.
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