The 71-run partnership is match-winning, a comeback that keeps India undefeated against Bangladesh in Tests.
Litton Das scores 73 and contributions from Nurul and Taskin lift Bangladesh from a precarious 113 for 6.
Rishabh Pant scored 93 and Shreyas Iyer scored 87 as India managed to score 314 runs in first innings taking a lead of 87 runs against Bangladesh.
Mominul scores 84 the lone bright spot for Bangladesh as they collapsed after tea.
India moved to the third spot in the ICC World Test Championship table with this win.
Hosts six down at 272 runs, at the end of the play, Shakib al Hasan (40*) and Mehidy Hasan Miraz (9*) were unbeaten for Bangladesh
The hosts were 42 for no loss at stumps, after India set 513-run target for Bangladesh in second Test.
India in commanding position in first Test against Bangladesh, lead by 271 runs after fiery spells from Siraj, Kuldeep.
Iyer and Pujara rise to the occasion and scored crucial half-centuries at a time when India was down and out.
Bangladesh crumbled under the scoreboard pressure as the Indian bowlers made merry to send the hosts packing for 182 runs