They will face Pakistan in the final on Saturday after the semifinals win in Nepal’s ANFA Complex on Thursday.
Regular goalkeeper Mitul Marma was out of the game after being sent off in the previous match against Nepal.
Bangladesh failed to get back in the game in the first half after Md Nazmul Ahmed Shakil’s shot went past the crossbar in the 37th minute.
Striker Md Ashikur Rahman scored the equaliser from the spot after Rasel Ahmed was fouled inside the box in the added time. It was his third goal of the tournament.
In penalty shootout, Md Raja Ansari, Md Rostom Islam Dukhu Mia, Tuhidul Islam Riday and Kamran Uddin Raju scored.
Bangladesh reached the semis topping the group with a 9-0 win over the Maldives and 2-1 victory over Nepal.
Goalkeeper Mehedi and striker Ashikur said they were focusing on the final against Pakistan now.
Coach Mostafa Anwar Parvez was a bit disappointed with chances missed in the match against India.
“Now it’s time to plan for the Pakistan match,” he said.