Chasing a daunting target of 459, Bangladesh were all out for 250 in 100.3 overs but put up a stiffer resistance than what the final outcome of the match would suggest.
The win was the Indian team's eighth victory in nine home Tests this season with the only draw coming against England at Rajkot.
This was India's the sixth successive series victory under Virat Kohli starting from Sri Lanka series in 2015. India's unbeaten streak in Test matches is now 19 with the last defeat coming against Sri Lanka in Galle back in August, 2015.
The Indian bowlers should be lauded for their collective effort as they had to show much more patience on a pitch that remained good for batting throughout the entire duration of the match.
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Spin twins Ravindra Jadeja (4/78 in 37 overs) and Ravichandran Ashwin (4/73 in 30.3 overs) shared the bulk of the spoils with Ishant Sharma (2/40 in 13 overs) -- all of whom worked tirelessly in pursuit of victory.
It was as controlled an effort one would see with an old ball. He hit his conventional back of the length with an occasional fuller delivery and some good short stuff.
With little help from the pitch his spell was a laudable effort. One such well-disguised short ball aimed at Shabbir Rahaman's (22) body forced him to play a pull-shot which he top-edged to the only fielder, Bhuvneshwar Kumar standing at fine leg boundary.
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Jadeja got his fourth when Taijul Islam (6) mistimed a pull-shot and was caught by KL Rahul.
Ashwin finished the match trapping Taskin Ahmed leg-before after Virat Kohli appealed for a DRS.
There was no celebration from the Indian players apart from customary handshakes as a few players collected the stumps as souvenirs.
The fifth day pitch was still good to bat on even though the turn on offer was comparatively more than the last four days.
In between, glorious shots and dead defence, there were moments of madness that became their undoing which showed why they need more experience at this level.
A better team on this flat track could have saved the Test match going in with seven wickets on the final day.
But as Kohli had pointed out before the game that one thing he has learnt is to be patient during dull phases of play.
Bangladesh may have fought well into the fifth day but India always had their foot firmly on the pedal throughout the entire duration of the match.
Skipper Mushfiqur Rahim's (23) undesirable shot selection, in fact, would have frustrated the dressing room just when he was having a reasonably good partnership of 56 runs with Mahmudullah.
Just like Shakib Al Hasan's indiscretion cost Bangladesh dearly in the first innings, Mushfiqur's intent was contrary to his risk-free nature in shot selection.