Rublev lost 7-6 (6), 7-6 (5) to Francisco Cerundolo and 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 and made it bleed.
The Russian player held the eighth and final qualifying place in the race for the Finals and could be overtaken by rivals.
U.S. Open runner-up Taylor Fritz became the fifth player to qualify for the Finals. The big-serving American reached the season-ending tournament for the second time in three years. The indoor event takes place from Nov. 10-17.
Fritz joined U.S. Open champion Jannik Sinner, Alcaraz, Alexander Zverev and Daniil Medvedev in the field.
Sinner
pulled out of the Paris Masters on Monday, citing a virus. The Italian player is guaranteed to finish the year as No. 1. He was the second high-profile player to pull out following
seven-time champion Novak Djokovic.
In remaining first-round play,
Holger Rune — who beat Djokovic in the 2022 final — advanced with a 6-4, 6-4 victory over Matteo Arnaldi.
No. 9 seed Alex de Minaur beat Mariano Navone 7-5, 6-1 to stay in outside contention for Turin, while No. 12 Hubert Hurkacz lost 6-1, 6-3 to Alex Michelsen.
U.S. Open semifinalist Jack Draper won 7-5, 6-2 against Jiri Lehecka; American Ben Shelton beat Corentin Moutet 6-3, 6-7 (8), 6-3, and Frenchman Giovanni Mpetshi Perricard hit 28 aces in defeating U.S. Open semifinalist Frances Tiafoe 6-7 (5), 7-6 (4), 6-3.
Fresh from his title in Basel, Mpetshi Perricard next plays Karen Khachanov and will look to add to his 512 aces.
Frenchman Arthur Fils also progressed by edging Croatian Marin Cilic 7-6 (5), 6-4 and next faces Jan-Lennard Struff.
