India Green, resuming the day at 98 for two and chasing an improbable 474-run target, were dismissed for 303 in their second innings with Sharma taking six for 94 to take his match tally to 10 for 133, his best figures in first class cricket.
The remaining four wickets in the Indian Green innings were taken by pacer Siddarth Kaul.
The impressive bowling performance from India Red came a day after captain Dinesh Karthik and Priyank Kirit Panchal slammed centuries to put their team in a strong position.
On the fourth and final day, India Green did put up a much improved showing with the bat but it was not enough to get even close to the victory target.
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Nair was their stand out batsman with 120 off 203 balls but his dismissal ended India Green's resistance.
The Karnataka batsman, who did not have the best of times during the recent India A tour of South Africa, was dogged in his approach.
Opener Ravikumar Samarth, who was batting on 46 by stumps on day three, fell early in the day for 59.
Mayank Dagar was the other batsman who showed some fight with 45 off 80 balls.
Brief Scores:
India Red 323 and 307/2 decl. India Green 157 and 303 in 89.2 overs (Nair 120; Sharma 6/94).