The 27-year-old Italian did not drop a set all tournament as he won the third title of his career and first on hard courts.
"This is an emotional moment for me because I had a tough year," Sonego said. "Now I'm going to enjoy this moment.
"I improved my tennis every day and I'm really happy for this match and this tournament."
The unseeded Sonego recovered from 40-0 down in the fifth game of the match and secured victory when the seventh-seeded Bublik sent a backhand return long.
The win will move Sonego up 21 places in the ATP rankings into 44th place.