Wiesberger was a runner-up twice last year in his first season on the European Tour but collected his first win in runaway style. He had three birdies in his final four holes for a 4-under-par 68 and a 72-hole total of 18-under 270.
He opened the tournament with a 72 Thursday but posted back-to-back 65s Friday and Saturday. He had two bogeys and a double bogey in the first round but played the final 54 holes without a bogey.
"I just tried to enjoy it and I had the three best rounds of my life," Wiesberger said. "I tried not to make bogeys and I did that pretty well. It was awesome."
Richie Ramsey turned in a 7-under 65 Sunday and finished second at 13-under while Victor Dubuisson (66) and Marcus Fraser (70) tied for third at 11-under.
Wiesberger opened Sunday's round with a five-stroke lead and had pars on the first four holes. He dropped a 6-foot birdie putt at the fifth hole before a string of nine consecutive pars.
Ramsay had pulled within two strokes by that point but Wiesberger made an 8-footer for birdie at 15 and a 20-footer at the par-3 16th for go back up by four. A 15-foot birdie putt at 18 accounted for the final margin.