Argentinian Diego Schwartzman moved within two wins of sealing a debut appearance at the ATP Tour Finals in London by beating Richard Gasquet to reach the Paris Masters third round on Wednesday, while Alexander Zverev and Daniil Medvedev also progressed.
The 28-year-old Schwartzman was too strong for France's Gasquet, taking a 7-5, 6-3 victory, and will next face Spanish qualifier Alejandro Davidovich Fokina in the last 16 at Bercy Arena.
Schwartzman will secure the final spot at the season-ending tournament by reaching the semi-finals in Paris, but would qualify even if he fails to do so, as long as neither Pablo Carreno Busta, Milos Raonic or Stan Wawrinka win the title.
"I have it in my hands but I have to say that I'm watching the other matches," said the sixth seed.
"I want to be there so I'm doing my best on court."
The Tour Finals get underway on November 15.
Schwartzman had never beaten Gasquet in three previous meetings, but the home player's first win since the US Open came in the opening round.
"Richard is such a player, he's always playing really good tennis," added Schwartzman. "I never beat him before so it was tough but I think I played a really good match."
Schwartzman reached his maiden Grand Slam semi-final at last month's French Open after making his first Masters final in Rome.
US Open runner-up Zverev continued his excellent run of form by cruising past Serbian Miomir Kecmanovic 6-2, 6-2 in under an hour.
The fourth-seeded German, who won back-to-back titles in Cologne last month, will face Adrian Mannarino in round three.
Zverev, who has won three Masters titles in his career, broke twice in each set to extend his winning streak to nine matches.
Third seed Medvedev reached the last 16 after Kevin Anderson retired injured from their encounter.
The Russian will next play Australia's Alex de Minaur, who beat Italian Lorenzo Sonego 6-3, 7-5, for a last-eight place.
South African Anderson quit when 5-2 down in an opening-set tie-break, with the tournament medical service saying the former US Open runner-up suffered a thigh injury.
The 24-year-old Medvedev is yet to reach an ATP final in 2020 after winning four titles and finishing runner-up five times last year.
But the world number five is set to gain ranking points in the French capital, after a second-round exit 12 months ago.
Raonic kept his slim Tour Finals hopes alive with a 6-4, 6-4 victory over Pierre-Hugues Herbert.
The Canadian, who lost the 2014 Bercy final to Novak Djokovic, plays 91st-ranked American Marcos Giron next.
Raonic's path through the draw has been made easier by early exits for seventh seed Matteo Berrettini and second seed Stefanos Tsitsipas.
Greek star Tsitsipas pulled out of the doubles event on Wednesday after saying he struggled with injury during his second-round loss to Ugo Humbert on Tuesday.
Davidovich Fokina backed up his first-round win over former champion Karen Khachanov by easing past Frenchman Benjamin Bonzi 6-4, 6-4, while Mannarino beat Japan's Yoshihito Nishioka in three sets.
Later on Wednesday, top seed Rafael Nadal starts his bid to win the title for the first time when he takes on fellow Spaniard Feliciano Lopez in the second round.