Serbia's Novak Djokovic overcame a challenging first set against qualifier Pierre-Hugues Herbert to reach the third round of the Paris Masters.
The world number two beat the 22-year-old Frenchman 7-6 (7-3) 6-3.
Djokovic saved two set points in the first set and saw off a rally from Herbert in the second before wrapping up victory in 93 minutes.
He was joined in the third round by home favourite
who beat Fernando Verdasco 7-5 (7-6) 6-3.
Gasquet's victory over the Spaniard boosts the world number nine's chances of qualifying for the season-ending ATP World Tour finals next month.
Five players - Rafael Nadal, Djokovic, David Ferrer, Juan Martin del Potro and Tomas Berdych - have secured their places for London, but three places remain.
- ranked 10th in the world - will not be at the O2 Arena next week after the Frenchman was beaten 1-6 7-6 (7-4) 7-6 (9-7) by Japan's Kei Nishikori.
World number seven
will qualify for the end-of-season event should be win his match in Paris on Wednesday, which will be against South Africa's Kevin Anderson or Russia's Mikhail Youzhny.
But there will be no British representatives in the finals after Dominic Inglot and Jamie Murray lost their respective doubles matches in Paris.