The 36-year-old saw off challenges from fellow Americans Andrew Putnam and Rickie Fowler, who had been the overnight leader. Bradley's last tour win was the BMW Championship back in 2018.
"I really put a lot of work in during this off season and this is what I want to do, I want to win tournaments, I want to play in Ryder Cups and I want to be in the conversation," Bradley told pgatour.com.
This is a good start."
Bradley claimed the lead with consecutive birdies at the sixth and seventh holes. A crucial birdie on the 17th gave him a two-stroke lead over Fowler and Putnam going into the final hole.
The Vermont native sealed victory with a par, finishing on 15 under for the tournament.
Meanwhile, for Fowler, the runner-up finish was his first since 2019 and his second top ten in recent times, marking a return to some form for the Californian.