Rahul went too deep in his crease while facing spinner Jeevan Mendis in the tenth over and dislodged the bails with his right foot.
That left Manish Pandey and Dinesh Karthik with a lot of work to do to get India over the line, they came together with 67 runs needed to win off 55 balls.
But a win would take India to the top, dislodging the Lankans. With captain Dinesh Chandimal suspended for the two upcoming matches in the tournament, for his team's slow over-rate against Bangladesh, Thisara Perera has been appointed the interim captain. After the 43-ball 118 he scored, incidentally against Sri Lanka, in December 2017, Sharma's scores in the following six T20Is have been: 27, 21, 0, 11, 0 and 17 (in that order), against various oppositions.
Bangladesh had come into the game having lost all four of their most recent limited-overs matches to Sri Lanka. Victor of the game will get 1-0 lead in the match and maintain its safer side in the series.
Bangladesh were ruled to be one over short of their target, so their captain Mahmudullah was fined 20 per cent of his match fee, and each of his players were fined 10 per cent.
But the left-hander looked in a hurry and in the process lost his wicket, chipping one straight to Thisara Perera at mid-off Nuwan Pradeep (1/30) as India slumped to 63 for three after seven overs.
KL Rahul (18), who came in place of Rishabh Pant, looked in good tough during his short stay before being dismissed in a odd manner.
India won the toss and chose to bowl first.
The Rohit Sharma led team bounced back from a disappointing showing against Sri Lanka with a comprehensive win against Bangladesh. With Sri Lanka looking to capitalize in the powerplay, Mendis played positively against both spin and pace.
Sri Lanka's charge was then briefly checked as Bangladesh introduced Mehedi Hasan Miraz in the seventh over that went for only three runs.
After 14 overs: India's score is 114 for 4.