Speedster Mustafizur Rahman dimissed Rohit Sharma for the third successive match, but India have coped well with the Bangladesh bowling in the first 15 overs of the third and final ODI on Wednesday.
The visitors now have 89/1 in 15 overs, with Shikhar Dhawan on 41 and Virat Kohli on 14.
Rohit looked strong, but Mustafiz made him give a catch behind the wicket after the opener made 29 off 29.
Winning the toss at the Sher-e-Bangla National Cricket Stadium, Tigers skipper Mashrafe Bin Mortaza invited India to bat first.
A win for the hosts will mean they make the extraordinary record of handing white-washes to opponents in three straight series.
The Tigers made a solitary change, bringing in Arafat Sunny in place of the injured Taskin Ahmed while India brought in Stuart Binny and Umesh Yadav in place of Ravindra Jadeja and Bhuvneshwar Kumar.