The 29-year-old had a bogey-free final round to win his maiden European Tour title. He finished at 9-under 279, two strokes ahead of Ireland's Damien McGrane.
Chowrasia surged into the lead with three birdies over the first four holes.
'This is the biggest achievement of my life, it's beyond my expectations,' said Chowrasia, the son of a greenskeeper at the Royal Calcutta Golf Club.
'I can't describe my emotions as it hasn't quite sunk in yet,' he said. 'Playing the last few holes, I realized the title was within my grasp.
'Playing safe and keeping my calm was important at that stage, so I kept my cool,' he said.
McGrane shot a 70 with three bogies and five birdies to finish two shots ahead of Jose Manuel Lara. The Spaniard had a 72.
Overnight leader Raphael Jacquelin of France shot a 74 to leave him five strokes back, in tied fourth with local Digvijay Singh.
World No. 4 and two-time U.S. Open champion Ernie Els shot a 71 and finished in a five-way tie for the sixth along with Thomas Bjorn, Gaurav Ghei, Maarten Lafeber and Ross McGowan.
Els was unable to recover from a disappointing opening round, which featured a quadruple-bogey 9.
The $2.5 million Indian Masters was jointly sanctioned by the Asian Tour on which Chowrasia plays regularly, but without previously winning a title.