The Latvian - seeded second at the ATP 250 event – was rarely troubled in his 6-1 7-6 (7-5) triumph on the clay.
Delbonis entered the final full of momentum after wins against top seed John Isner and Gilles Simon.
But he made a disastrous start, losing the last five games of the first set as Gulbis starred on serve.
He won every single one of his points on first serve in the opener and Delbonis simply had no answer for the world number 19.
To his credit, Delbonis regrouped in the second set, and despite Gulbis continuing to star on serve, he remained in the contest.
There were no breaks in the second, forcing a tie-break, and Gulbis showed his big-game experience to claim victory.
The 25-year-old has now won all of the ATP Tour singles finals he has contested.
He begins his French Open campaign with a clash against Poland's Lukasz Kubot, while Delbonis starts against Serbian Dusan Lajovic.