Gasquet was down a set and 5-3 in the second set before reeling off four consecutive games to even the match. That sent him off to a 5-7, 7-5, 6-4 victory over Grigor Dimitrov. The decision allowed Gasquet to improve to 3-0 lifetime against Dimitrov.
Dimitrov fired 21 aces and hadn't dropped his serve until Gasquet broke him to make the score 5-4 in the second set and get back in the match.
Gasquet's comeback allowed seeded players to go 5-1 in second-round matches Thursday in Bangkok. Gael Monfils, with a 7-5, 7-5 win over sixth-seeded Viktor Troicki, was the sole exception.
Also Thursday, fourth-seeded Gilles Simon had a pair of breaks in each set of a 6-4, 6-4 win over Go Soeda and No. 8-seeded Bernard Tomic fought off 11-of-13 break points in a 4-6, 6-3, 6-4 defeat of Dudi Sela.
Friday's quarterfinal schedule calls for Verdasco to face top-seeded Janko Tipsarevic while Monfils goes against Simon. Raonic draws No. 7 Jarkko Nieminen and Gasquet plays Tomic in the other quarterfinals.