India lost Rohit and Dhawan early after being asked to bat.
Rahul struck 52 to get the innings going.
Shreyas Iyer smashed 62 off 33 as India posted 174 for 5.
Deepak Chahar got two in two early as Bangladesh got off to a poor start.
Naim (81) and Mithun (27) smashed 98 for the third wicket to keep Bangladesh in the chase.
Shivam Dube dismissed Rahim, Naim and Afif Hossain to bring India back in the game.
Deepak Chahar picked up a hat-trick in the last over and registered the best figures in T20Is as he ended with 6 for 7. Bangladesh lost by 30 runs and conceded the series 1-2.