Bublik saved all three break points he faced and hit 28 winners to 18 for Fils in the final.
"When we won the second title with my coach, I said: 'Maybe that's it, maybe I will never win one more.' It was the greatest feeling ever," said Bublik.
"So, being here again, winning another title, it means the world for me."
Bublik won his first title in Montpellier, France, in 2022 and his second on the grass in Halle, Germany earlier this year.
In their first meeting, Bublik capitalised on a couple of unforced errors by the young Frenchman to break for a 3-2 lead. He saved a break point in the eighth game with a forehand winner before concluding the opening set with an ace.
Fils, the youngest finalist in the tournament's history at 19, had a poor start to the second set, dropping serve by sending a forehand into the net. Out of frustration, he smashed his racquet into the ground.
Bublik then saved two break points at 3-2 with an ace and a service winner. Fils saved two match points, but the Kazakh converted the third with his 11th ace.
Bublik was going through a poor run of form before this tournament, losing five straight matches on hard court.
