Playing on his home course at the Delhi Golf Club, the 35-year-old Kapur carded a final-round four-under-par 68 for a winning total of 17-under 271.
"It's an amazing feeling," an emotional Kapur told reporters. "This victory has not really sunk in yet but when I was walking down the 18th, I was really trying to hold back the emotions.
"I was telling myself just finish the race, finish the race and it's just amazing to be able to do it."
Only a shot separated the players at the top of the leaderboard before Kapur pulled away from the chasing pack with four birdies in five holes, starting from the 11th.
Kapur's two previous Asian Tour titles came at the Volvo Masters of Asia in Thailand in 2005 and at the Yeangder Heritage in Taiwan this year.
"To be able to win in front of all my friends and family is wonderful. I grew up playing golf here and told myself I got to win at the Delhi Golf Club one day," Kapur said.
"So no words can actually describe how I'm feeling right now. The reception I got when I was coming up the 18 was just amazing. It was well worth the wait."
Overnight joint leader Paul Peterson of the United States finished tied for second place on 14 under with six other Indians.
(Reporting by Sudipto Ganguly in Mumbai; editing by Ed Osmond)
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