Aiming for his second title on home soil, Gasquet trailed 4-1 in the deciding set and asked the trainer twice to massage his fatigued legs.
"I was very close to losing," Gasquet told Sport Plus television. "I was extremely tired in the third set. I had pain in my knees."
The unseeded Gasquet broke to trail 4-3 on a wide backhand from the second-seeded Verdasco, who swore loudly in Spanish at the changeover.
In the next game, just after Gasquet hit a double fault, Verdasco antagonized the French crowd that was booing him by raising his arms in the air as if asking for more jeers. Verdasco broke Gasquet for 5-3 but failed to serve out the match. Gasquet finally overtook Verdasco in the tiebreaker after 2 hours, 38 minutes.
A former top-10 player, the 68th-ranked Gasquet was looking to get back to his best level after his career was hit by a suspension last year for testing positive for cocaine.
"I'm really very happy," Gasquet said. "It's my sixth title. It's been a long time since I've won a tournament of that caliber."
His previous triumph was at Mumbai in 2007.
The Frenchman took Verdasco's serve in the sixth game and did not allow any break chances in grabbing the first set with a forehand winner.
Verdasco netted an approach shot to hand Gasquet a 5-4 lead in the second set, but the Frenchman failed to serve out, letting Verdasco immediately break back. Verdasco then hit two forehand winners in a row to level at one set apiece.
Verdasco was trying to win his sixth career title and third this year.