The hosts won the opening Test also inside three days, as well as the preceding Twenty20 series 2-1
Pacer Umesh Yadav claimed five wickets as India thrashed Bangladesh in just over two days of their first day-night Test to sweep the series 2-0 on Sunday.
Bangladesh were bowled out for 195 in less than an hour of the first session on day three in Kolkata, as India won by an innings and 46 runs to record their 12th-straight Test series triumph on home soil.
It was a memorable pink-ball international debut for India, who became the only team to win four consecutive Tests by an innings margin.
Virat Kohli's side consolidated their top position in the World Test championship with three successive series sweeps.
Mushfiqur Rahim made a valiant 74 before falling to Yadav, and the innings soon folded as Mahmudullah did not return to bat after he had retired hurt on 39 on day two.
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India took 8.4 overs to wrap up the game at Eden Gardens with Yadav taking all the three wickets to fall Sunday afternoon.
Ishant Sharma led the pace charge with impressive match figures of 9-78 to flatten the Bangladesh batting that fell for 106 in their first innings of the opening day.
Kohli played a key part with his 136 in India's 347 for nine declared on Saturday as they managed a lead of 241 runs.
The tourists were in early trouble at 13 for four in the final session on day two when Mushfiqur resisted India's persistent pace attack.
Ishant trapped Shadman Islam lbw for nought and then claimed skipper Mominul Haque, who got a pair of ducks.
The spearhead quickie, who claimed five wickets in the first innings, bowled at a lively pace as one of his rising deliveries hit Mohammad Mithun on the helmet.
Bangladesh were forced to take two concussion substitutes in Mehidy Hasan and Taijul Islam for Liton Das and Nayeem Hasan who were hit on the helmet by Shami on day one.
Mushfiqur was also at the receiving end of a nasty hit from Yadav, but went on to play a fighting knock.
Kohli completed his 27th century before falling to a stunning catch by Taijul off Ebadat Hossain.
India won the opening Test also inside three days, as well as the preceding Twenty20 International (T20I) series 2-1.