The 19-year-old Argentine unleashed a huge serve on his first match point. Gasquet managed to return it, but del Potro was ready to put away a forehand winner.
Along with his first title, del Potro also collected a white luxury convertible presented by the tournament sponsor.
"This is incredible. I've dreamed of winning a tournament since I've been a kid and now I also get a car," said del Potro, who drove the vehicle around the court after the awards ceremony.
He also picked up euro118,000 (US$186,853) as first prize.
"I congratulate Juan Martin but he'd better be careful, it's a fast car," Gasquet joked.
Del Potro broke serve for a 5-4 lead and served out the first set.
After a brief rain break, he again broke Gasquet's serve to take a 6-5 lead and served out the match at love.
Del Potro, who entered the event ranked No. 65, beat four seeded players to win the tournament.
Rafael Nadal, who won the event last year, pulled out with a knee injury after winning Wimbledon.
