This was the former French number one's eighth career title and his first since Mumbai in September 2007.
The unseeded Gasquet, who was following up his success in a minor event in Bordeaux last week, said: "I'd like to thank the fans who really helped me in the third set."
Former world number seven Gasquet, currently 68 in the rankings, converted his first break point opportunity in the sixth game before going on to take a 5-2 lead with a service hold to love.
In the eighth game, Verdasco saved four set points overall. Gasquet won 23 of 31 service points to clinch the first set in 43 minutes.
Verdasco took a 3-1 lead in the second set, but then lost four of the next five games. Serving for the match at 5-4, Gasquet dropped his serve to love.
Verdasco grew in confidence, levelling the scoreline at one-set apiece in a run of six straight games to a 3-0 lead in the third set.
He came within one point of taking a 5-1 lead, but could not convert a break point opportunity on Gasquet's serve.
Verdasco served for the match at 5-3, but was broken to 15. There were five breaks of serve in the third set, which was decided on a tie-break.
Gasquet, who suffered from leg cramping in the third set, converted his first match point at 6-5 in the tie-break when Verdasco hit a forehand wide.