Needing a par on the 18th for victory, Bradbury found himself off the green with his second shot, but a superb chip took him to within a foot of the hole.
South African Casey Jarvis had won the last two DP World Tour events but was denied a hat-trick when he finished a shot back with a final round 66, tied for second with Englishman Brandon Robinson-Thompson, who also managed a 66.
"I thought I had lost in on the front nine, I had so many chances and did not take them," Bradbury said. "But it feels really good to put it together on the back nine."
"Casey and Brandon played amazing, it was pretty tight but I somehow managed to get it done in the end."
Bradbury earns a third win on the European tour, his first coming at the 2022 Joburg Open. He also claimed victory at the 2024 FedEx Open de France.