Kei Nishikori of Japan beat Jo-Wilfried Tsonga 1-6, 7-6 (4), 7-6 (7) in the second round of the Paris Masters on Tuesday, ending the Frenchman's bid for a spot in the World Tour Finals.
Gasquet outlasted Fernando Verdasco 7-5, 6-7 (6), 6-3 in another second-round match to stay in contention for the tournament in London.
In the tiebreaker of the final set, the eighth-seeded Tsonga wasted his first match point by double-faulting. Nishikori fired an ace to save a second match point and then won the match when Tsonga made his eighth double-fault.
Nishikori blew a 4-1 lead in the second set but he capitalized on a string of unforced errors from Tsonga in the tiebreaker to level the match.
Meanwhile, the ninth-seeded Gasquet converted his fifth match point when Verdasco sent a backhand long.
Verdasco hit two service winners to save two match points at 6-5 in the second set. The Spaniard then erased seven break points in the final set before dropping serve at 3-all with a wide forehand.
Rafael Nadal, Novak Djokovic, David Ferrer, Juan Martin del Potro and Tomas Berdych have already qualified for the tournament in London next week. There are three spots up for grabs as Andy Murray withdrew from the season-ending event to recover from back surgery.
In first-round matches, Grigor Dimitrov of Bulgaria rallied past two-time semifinalist Michael Llodra of France 6-7 (5), 6-3, 6-3, and Spanish lucky loser Pablo Andujar overcame Vasek Pospisil of Canada 6-4, 2-6, 6-4.
Dimitrov broke for 4-2 in the final set and hit a forehand volley winner on match point. He became the first Bulgarian to win a title on the ATP Tour at the Stockholm Open earlier this month.
Andujar replaced Gael Monfils in the main draw after the Frenchman pulled out because of a left wrist injury.
Kevin Anderson of South Africa, Marcel Granollers of Spain, Ivan Dodig of Croatia, French wild card Nicolas Mahut and Polish qualifier Michal Przysiezny also moved into the second round.
Anderson was leading 4-6, 7-6 (0), 2-1 when his opponent, Mikhail Youzhny of Russia, retired because of pain in his right elbow.
Meanwhile, Granollers will face top-seeded Rafael Nadal after his 6-4, 6-4 victory over Dmitry Tursunov of Russia. Dodig beat Edouard Roger-Vasselin of France 7-6 (6), 6-4, Przysiezny defeated Jarkko Nieminen of Finland 6-3, 7-6 (6), and Mahut downed Alexandr Dolgopolov of Ukraine 7-6 (6), 6-1.
