Gulbis needed a first-set tiebreaker then rolled in the second set, notching a 7-6 (7-3), 6-3 victory over the Frenchman in a 1-hour, 36-minute affair.
Gulbis, who also claimed the 2010 Delray championship, was down 4-5 in the first set before rallying to the victory, improving to 3-0 record in ATP World Tour finals.
He became the first qualifier to win a tour event since Jarkko Nieminen claimed the Apia International Sydney in January 2012.
The 29-year-old Roger-Vasselin was appearing in his first career final.
Notable deaths of 2014 [PHOTOS]