Gasquet triumphed 6-3, 3-6, 6-2 and will meet his eighth-seeded countryman Benoit Paire in Sunday's championship match.
Gasquet improved to 13-1 for the year and will be playing for his second title of the season when he squares off against the 23-year-old Paire.
Paire also needed three sets to make the finals. He rallied after losing the first set and prevailed over Michael Llodra of France 4-6, 6-3, 6-1.
Paire scored 17 aces Saturday and broke Llodra's serve four times.