Chasing a daunting target of 459 runs in the 4th innings, Bangladesh were bundled out for 250 in 100.3 overs on the 5th and final day at the Rajiv Gandhi International Stadium.
But the visitors put up a stiffer resistance than what the final outcome of the match would suggest. The win against Bangladesh was India's 8th victory in 9 home Tests this season with the only draw coming against England at Rajkot.
This was India's 6th 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 in August, 2015.
For a team ranked world No. 9 in ICC rankings, Bangladesh hung on for four days and two sessions - something that nobody had expected from the minnows.
India's spin twins Ravindra Jadeja (4/78 in 37 overs) and Ravichandran Ashwin (4/73 in 30.3 overs) shared 8 wickets in the second innings. Pacer Ishant Sharma (2/40 in 13 overs) was excellent and got the remaining 2 wickets for India.
With this latest success, Kohli surpassed former skipper Azharuddin's record. The 28-year-old Kohli is now the 3rd most successful Indian captain behind Mahendra Singh Dhoni and Sourav Ganguly. Today's was Kohli's 15th win as captain in 23 Tests.
The visitors played close to 230 overs, both innings included. 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.
Bangladesh needed to bat out 58 overs in the last 2 sessions to save the match but Ishant's brilliant post-lunch spell put paid to any hopes that the visitors had harboured.
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.
He then bowled an in-swinger that looked like reverse to find Mahmudullah Riyadh (64) plumb in-front. With Mahmudullah's departure the writing was clearly on the wall for the visitors.
Mehedi Hasan Miraz again played 60 balls for his 23, was the eighth batsman out with Jadeja's delivery kicking up sharply to induce an outside edge snapped by Wriddhiman Saha.