Bublik, 28, continued his form from last year in which he triumphed in Halle, Gstaad, Kitzbuehel and Hangzhou following a dramatic turnaround that also saw the Kazakh player reach his first major quarter-final at Roland Garros.
"I have no words. The only goal for this season was to achieve the top 10 and in the first week, I am winning the title and I have made the top 10," Bublik said.
"If you told me that last April, I would have never believed you. For me standing here, it is a big pleasure and I hope to continue in the same way."
Both players started effectively behind serves with Bublik taking charge from the baseline, but his erroneous drop shots helped Musetti maintain a close reach and pushed the first set to a tie-breaker.
Bublik dominated in volleys in the tie-breaker to take the first set, and then displayed tremendous speed and athleticism to counterattack against the Italian, who required treatment on his right arm as the match progressed.
With improved drop shots and a solid defence at the baseline, Bublik dominated in the second set and claimed his ninth ATP Tour title with Musetti sending a return into the net.
Musetti, who was chasing his first title since he won two in 2022, has ensured a top-five berth, his career-best, on Monday, despite not winning the title.