West Indies skipper Jason Holder has been ruled out of the upcoming tour to Bangladesh due to a shoulder injury.
Dhawan (92) and Rishabh (58) scored superb fifties to guide the team home in the last ball of the thrilling match.
The host beat Bangladesh by 60 runs in their opening game in Women World T20.
India crushed West Indies by 71 runs in the second T20I played at the Atal Bihari Vajpayee Ekanta Stadium in Lucknow.
High-flying India overpowered West Indies in the first T20I of the three-match series at the Eden Gardens on Sunday.
Depleted West Indies search for redemption in natural habitat.