Dhawan put on a crucial 130-run third wicket stand with Rishabh Pant, who hit 58, to bring India close to their target of 182 before West Indies hit back in Chennai. Yuzvendra Chahal (2/28) and Washington Sundar (1/33) have been decent with the ball.
It was left to Manish Pandey to strike the winning run off the last ball, which the 29-year-old did with no great conviction.
Unbeaten N Pooran top scored for the West Indies with 53 while DM Bravo with 43 also remained unbeaten. Shikhar Dhawan was instrumental in India's win, deservedly earning the Man of the Match award for his 92-run knock.
India vs West Indies 3rd T20I between India and West Indies is being telecast on Star Sports 1 and 1 HD, Hindi 1 and Hindi 1 HD and Tamil 1.
Shimron Hetmyer and Shai Hope laid the foundation with a 51-run partnership. But Pant had already done the damage before giving up his wicket as India cruised past Windies in a sensational last-ball win.
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Reeling after two crushing defeats, the West Indies showed the stomach to fight as they batted with a lot more goal here.Pooran, who has been on the fringes for a while and did well in the Caribbean Premier League (CPL), showed why he is rated highly, batting with a lot of enterprise.He wasn't afraid to go for his shots and also employed the switch-hit on a few occasions, including hammering a six off Chahal.
Chahal, who got a lot of turn, was the most successful Indian bowler with 2 for 28 from four overs, but faced the heat towards the end when Pooran and Bravo went on the attack.
Hope had looked like carrying on to a big total when he skied a delivery from Yuzvendra Chahal into the hands of Washington Sundar who took a good catch at long on to be out for 24.
Denesh Ramdin and Darren Bravo then added 32 in four overs before Ramdin tried to give himself room to smash Sundar through the offside and was bowled.
The result caps off a complete domination by India, who had won the Tests 2-0 and then the one-day worldwide series 3-1 against the visiting West Indians.