In the quarterfinals, Gasquet, whose only career title came in this tournament in 2005, beat fellow Frenchman Gilles Simon, 6-3, 6-1.
The 20-year-old Gasquet, who ran his record in this event to 8-0, improved to 10-13 in 2006, advancing to the semifinals of an ATP event for the first time since last year's win.
He had only three aces on his serve, but broke Simon in five of his nine chances.
"It's getting better (for me) and I'm really happy (to have reached the semifinals)," Gasquet said.
"It was really difficult to play Gilles because he's a good friend and also because the conditions were so difficult due to the wind."