The native of South Africa, who now lives in England, had a final total of 13-under 263. Sterne was five shots behind the nine players tied for the lead at 4-under 65 after Thursday's first round.
He finished with birdies at six of his final 12 holes, including the 18th, to beat Welshman Bradley Dredge (67), Danes Vibe-Hastrup (66) and Soren Kjeldsen (65) and Singapore's Mardan Mamat, whose 7-under 62 Sunday was the week's best score for one round. That group finished 12-under 264.
"I didn't play the last hole well," Dredge said.
He was a co-leader after Saturday's third round and was attempting to become the first Irishman in 25 years to win the tournament.
"Bradley has been close a few times, but unfortunately that is how it goes," Sterne said.