Left-hander Dube gave a good account of himself ahead of the T20 World Cup in June with an unbeaten 60 off 40 balls to help India overcome a 159-run target with 15 balls to spare.
Electing to field, India restricted Afghanistan to a modest 158-5.
Rahmanullah Gurbaz (23) and Ibrahim Zadran (25) put on a 50-run opening partnership but it was Mohammad Nabi's 42 off 27 balls that helped Afghanistan cross the 150-mark.
Left-arm spinner Axar Patel led India's disciplined bowling effort, claiming 2-23 in his tidy four overs.
The home side were rattled early in their chase with skipper Rohit Sharma, playing his first T20 International in more than a year, run out for a duck in the first over.
Rohit drove the ball to mid-off and embarked on a quick single but Shubman Gill at the other end was busy watching the ball leading to an almighty mix-up that led to his captain's dismissal.
Gill struck 23 but was stumped after he came dancing down the track only to miss the delivery from off-spinner Mujeeb Ur Rahman.
Tilak Varma (26) combined with Dube in a breezy 44-run stand to steady India but departed after Gulbadin Naib took a blinder at backward square leg.
Jitesh Sharma fell after a quickfire 31 but Dube could not be denied his half-century, which came in 38 balls, and he celebrated the milestone with a monster six before sealing their victory with a four.
The teams move to Indore for the second T20 of the three-match series on Sunday.
