The 42-year-old carded a one-under 71 for a 11-under 277 after he was in a three-way tie for the lead going into the final day at the picturesque valley course near Mumbai.
Buhrmann and fellow overnight leader Simon Hurd appeared headed for a playoff until the Briton dropped two strokes on the penultimate hole, carding 73 to come second at nine-under 279.
Hurd found the rough off the tee on the 17th effectively to end his contest with Buhrmann, who never looked back after he sank an eagle on the 12th and coolly parred the last four holes.
Australian Terry Pilkadaris (70) was one shot behind Hurd, moving up three places to finish third while an even par round gave compatriot Marcus Both fourth place at five-underoverall.
Indian hope Ashok Kumar, joint overnight leader, lost seven shots on the inward nine to card 78, eventually tying for fifth with Australian Kane Webber (75) and South Africa's Simon Griffiths (77) and Garth Mulroy (72).
Buhrmann was delighted after years of frustration, including four second-place finishes in Asia.
"I said earlier in the year to some people that you know what, my dream is to win on the Asian Tour before I die", he said.
"They really laughed at me but I really meant it. A few months later, I've got my dream come true," he said.
Hurd, a former European Tour regular, took the disappointment in his stride.
"The double on 17 did me in," he said. "But to be fair, Hendrik deserves it. He's 42 years old and he deserves it as he's a nice guy."