Roger Federer was beaten 5-7, 5-7 on the opening day after Novak Djokovic had swatted aside debutant Matteo Berrettini in the earlier Group Bjorn Borg contest.
The "Big Three" remain the men to beat at the season-ending ATP Finals in London.
Novak Djokovic and Roger Federer were drawn in the same group for next week's climax to the season, the ATP Finals.
Roger Federer will next play at the ATP Tour Finals in London, which get underway on November 10.
Marin Cilic and Jo-Wilfried Tsonga reached the second round after Roger Federer withdrew from the Paris Masters on Monday.
Novak Djokovic and Rafael Nadal put their immediate aims to one side and played a practice session in Paris.
Roger Federer said he was withdrawing from this week's Paris Masters in order to "pace" himself for the next year.
Roger Federer is due to play next week at the Paris Masters, the final event of the regular season before the November 10 start of the ATP Finals in London.
Roger Federer will be playing for his 10th title at his home tournament when he faces Alex de Minaur in a first-time meeting.
Top seed Roger Federer, chasing a 10th title at his hometown event, will receive a walkover into Saturday's semi-finals.
Roger Federer won his 22nd match in a row at the Swiss Indoors and earned a quarter-final place at his home event for the 17th time.
Roger Federer is third in the world rankings, while Rafael Nadal and Novak Djokovic won all four Grand Slams between them this year.
Roger Federer, who has won a doubles gold alongside fellow Swiss Stan Wawrinka, is still waiting to get his hands on an Olympic singles gold.
Roger Federer was penalised after twice hitting the ball out the court in anger.
Roger Federer plays Alexander Zverev after the young German beat Andrey Rublev of Russia, 6-0, 7-6 (7/4).
Roger Federer had asked fans to suggest a new display picture and was met with hilarious responses
Arbaaz Khan has often been called Roger Federer's doppelganger on social media and that is why some fans asked him to watch the Bollywood actor's movies.
Roger Federer was seen coaching Rafael Nadal at the Laver Cup as Team Europe captain Bjorn Borg watched on.