Fitzpatrick hit five birdies on the back nine and eight overall on day four to topple overnight leader Eugenio Chacarra of Spain at the DLF Golf and Country Club in Gurgaon.
Fitzpatrick, 27, was behind last year's winner Chacarra by four shots at the end of day three but bested the tough course in round four with good drives and putts.
"I'll try and explain (how it feels) without crying, it's been a lot of hard work for a long time," said an emotional Fitzpatrick, who finished at nine under overall.
"Over the moon, probably going to cry, but yeah, ecstatic."
The Englishman joins his elder brother, European Ryder Cup star Matt Fitzpatrick, as a winner on Tour. The siblings made history as the first ever to win in successive weeks on the DP World Tour and the PGA Tour.
Matt is a 10-time winner on the DP World Tour, most recently at the World Tour Championship in November, and also won last week's Valspar Championship on the PGA Tour to climb to a career-high world number six.
"I see my mum and dad tomorrow and we're going to meet my brother in Florida," Alex said.
"It's been a good few weeks for the Fitzpatricks."
Chacarra was second after hitting three over in the final round.
South Africa's M.J. Daffue carded five under to finish joint third with Frenchman Ugo Coussaud and England's Andy Sullivan.