Bradbury carded a five-under-par 65 to finish on 17 under overall, edging South Africa's Casey Jarvis and England's Brandon Robinson-Thompson, who shared second place on 16 under after rounds of 66.
The Englishman needed a par on the final hole to win but his approach ran over the back of the green. He responded with a superb chip that rolled to within inches of the cup before tapping in to seal victory.
"That chip on 18 - I'm not known for my short game so I was really pleased with that one. I was literally shaking over it and I'm really happy it came out like it did," Bradbury said.
The closing stretch saw several contenders falter. Hennie du Plessis began the day with the lead but slipped out of contention after two bogeys and a double bogey on the par-three 15th, eventually finishing fourth.
Robinson-Thompson also threatened to win before a three-putt bogey on the 18th dropped him back, while Jarvis narrowly missed a birdie putt on the final hole that would have forced a playoff.
"I thought I had lost it on the front nine. I had so many chances and didn't take them, but it feels really good to put it together on the back nine," Bradbury said.
The victory adds to Bradbury's 2022 Joburg Open triumph and his win at the Open de France in 2024, making him just the third multiple winner of the tournament alongside Charl Schwartzel and Richard Sterne.
Jarvis had been chasing a third consecutive win after triumphs at the Kenya Open and South African Open, a feat previously achieved only by Nick Faldo and Seve Ballesteros.
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