With this victory, India now have a 1-0 lead in the two-match Test series.
Team India beat Bangladesh by an innings and 130 runs to take a 1-0 lead in the first of the two-match Test match series on Saturday at the Holkar Cricket Stadium.
This was also the sixth consecutive win for the home side in red-ball cricket.
India now have also secured their top spot on the ICC World Test Championship points table with 300 points.
Bangladesh on trail of 343 runs, got off to a patchy start on the third day as both openers, Imrul Kayes and Shadman Islam, were dismissed within opening seven overs.
Mohammad Mithun and Mominul Haque soon took over the charge but managed to score just seven runs before Mohammed Shami's quicker delivery got rid of him and Mithun (18).
Mahmudullah and Mushfiqur Rahim were next to bat and they managed to knit together a 28-run partnership before Shami removed Mahmudullah for 15 runs.
Liton Das came in and settled in quickly and formed a 63-run partnership with Rahim.
However, Indian off-spinner Ravichandran Ashwin handed the home side with a key breakthrough with his caught and bowled effort to remove Das for 35 runs.
Rahim was the only "Bengal Tiger" batsman who actually settled into the playing conditions of Indore.
He also secured his half-century and built up 59 runs with Mehidy Hasan before pacer Umesh Yadav knocked the sumps of Hasan (38) to ship India ever so closer to the victory.
Taijul Islam innings was short-lived too as he departed after adding just six runs to the total before giving away an easy catch to a floated Mohammed Shami delivery.
Just moments after this, Rahim (64) too was sent back to the dressing room by Ashwin who delivered the final blow by dismissing Ebadat Hossain to hand India the victory.
While Mohammed Shami picked up four wickets on the day, Ashwin secured three with Umesh Yadav taking two and Ishant Sharma bagging one wicket for their troubles.
Earlier in the day, India declared their first innings at 493/6. Mayank Agarwal smashed the second double century of his career as he scored 243 runs.
Ajinkya Rahane (86), Ravindra Jadeja (60*) and Cheteshwar Pujara (54) also scored half-centuries.
On the first day of the match, Team India had bowled through the Bangladeshi batting line up for 150 runs.
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