The Frenchman, who played in the year-end championships once before in 2007, sits in ninth place in the standings, a mere 20 points behind Stanislas Wawrinka for the last spot in the eight-man field.
Pospisil is having a breakthrough year, reaching his maiden Masters semifinal in Montreal and helping guide Canada to the Davis Cup semifinals for the first time last month.
The six-foot-four native of Vernon, B.C., overpowered Gasquet with his forehand and serve, hitting 16 winners to just two for the Frenchman in the opening set and finishing with 10 aces.
"The key was to stay aggressive the whole time, even in the big moments, going for my shots," Pospisil said. "It's a huge win for me."
Pospisil was joined in the second round by Milos Raonic of Thornhill, Ont., who served 16 aces to defeat Polish qualifier Michal Przysiezny 6-4, 6-4.
The 10th-seeded Raonic is making a late-season run at qualifying for the ATP Finals, as well, reaching back-to-back finals in Bangkok and Tokyo the last two weeks. He won the title in Thailand but lost to Juan Martin del Potro in Japan.
He's 10th in the standings for the ATP Finals, trailing Gasquet by less than 300 points.
"I've had two great weeks leading into this one and forced myself and pushed myself to do well this week," he said.
Former No. 1 Lleyton Hewitt jumped out to 3-0 against Andreas Seppi before the Italian reeled off 10 of the next 11 games to win the match 6-4, 6-2.
Seppi will play 17-time Grand Slam champion Roger Federer in the next round.
Hewitt is working his way back up the rankings after five surgeries in recent years and was coming off an upset win over del Potro at the U.S. Open.
The Australian said his wrist has been bothering him in recent weeks and he'll undergo tests to determine the extent of the injury. "I've just had a bit of a niggle," he said.
Play was disrupted for the second straight day by the remnants of Typhoon Fitow, which made landfall in southern China early Monday and dumped 15 centimetres of rain on Shanghai, the highest single-day total since 1961.
Matches in the main stadium were played with the roof closed, while those scheduled for outer courts were moved to an indoor facility so organizers could attempt to finish the first round on Tuesday.
In other matches, 12th-seeded Kei Nishikori of Japan defeated Grigor Dimitrov of Bulgaria 6-3, 6-4, Tommy Robredo of Spain beat countryman Albert Montanes 6-4, 6-1, Benoit Paire of France upset 13th-seeded countryman Gilles Simon 6-4, 6-3, and Frenchman Jeremy Chardy ousted Australian Bernard Tomic 7-5, 6-2.
Rafael Nadal, who reclaimed the No. 1 ranking this week, and Novak Djokovic are scheduled to play their opening matches on Wednesday.