Nitish and Rinku assault came after India lost top three batters in the powerplay.
Earlier, Bangladesh skipper Nazmul Hossain Shanto won the toss and opted to bowl against unchanged India.
Bangladesh made one change to their playing XI, bringing in Tanzim Hasan Sakib for Shoriful Islam.
India lead the three-match series 1-0.
Playing XIs
India: Abhishek Sharma, Sanju Samson (wk), Suryakumar Yadav (capt), Riyan Parag, Nitish Kumar Reddy, Hardik Pandya, Rinku Singh, Washington Sundar, Varun Chakravarthy, Mayank Yadav, Arshdeep Singh
Bangladesh: Litton Das (wk), Parvez Hossain Emon, Najmul Hossain Shanto (capt), Towhid Hridoy, Mahmadullah, Mehidy Hasan Miraz, Jaker Ali, Rishad Hossain, Tanzim Hasan Sakib, Taskin Ahmed, Mustafizur Rahman.