Barring their opening loss to Sri Lanka, India have had a successful tournament so far, winning the remaining matches and thereby topping the points table with six points.
Bangladesh bounced back on to post a respectable total of 166-8 from 20 overs in the final of the Nidahas Trophy against India here on Sunday.
The Indian team looked in good touch, with opener and stand-in skipper Rohit Sharma scoring 56 off 42 deliveries.
India started the chase well but stumbled midway and needed 34 runs off the last two overs when Karthik came out to bat.
8 - Washington Sundar has taken eight wickets in Sri Lanka in T20Is - the most by a player before the age of 20.
The match went down to the wire, with India needing 12 runs to win from the final over. Mustafizur Rahman then bowled a masterly 18th over, when his first five balls at Vijay Shankar yielded only one run and Manish Pandey (28) perished off the sixth trying to accelerate the contest.
After Jaydev Unadkat got him and Rubel Hossain off back-to-back deliveries in the 19th over, Bangladesh appeared to be losing the plot but Mehidy Hasan took 18 runs off the last over bowled by Shardul Thakur to guide this team to 166/8. He and KL Rahul (24) found it easy going against the Bangladesh bowlers until Sharma went for a fatal slog-sweep of Nazmul Islam, departing with three sixes and four boundaries to his name.
Earlier, Sabbir Rahman's magnificent 77 and Mehidy Hasan Miraz's last-over cameo have helped the Tigers to set India a modest target of 167 in the final of the T20I tri series.
Yuzvendra Chahal then dealt the biggest blow, sending Tamim Iqbal (15) and Soumya Sarkar to the pavillion in the space of three balls.
WICKET! Yuzvendra Chahal has just got his second wicket in his first over as he sees off Soumya Sarkar.
WICKET! Shakib Al Hasan provides Bangladesh with the crucial breakthrough as he removes Shikhar Dhawan. His eight ball knock included two fours and three sixes and he was adjudged Man of the Match.
The Men in Blue made one change, bringing back Jaydev Unadkat in place of Mohammed Siraj.