Brown's total of 18-under 270 gave him his first victory on the European Tour. He had won an event on the Asian Tour last week.
"The last two weeks have been a blur," Brown said.
The New Zealander trailed through the final round until the string of birdies gave him the lead at No. 15.
Taichiro Kiyota of Japan and Australians Greg Chalmers and Scott Strange tied for second-place at 15-under-par 273. Kiyota, who led after the third-round, slipped to 71 on the final 18 holes. Strange shot 67 and Chalmers 68.