India dealt with some middle-order resistance before wrapping up an innings-and-130-run win over Bangladesh on day three in Indore to move 1-0 up in the two-Test series.
Virat Kohli declared overnight with India, thanks principally to Mayank Agarwal's 243, having reached 493-6 at stumps on day two after skittling the Tigers for 150 on the opening day at Holkar Stadium.
Bangladesh slumped to 72-5 in their second innings but then held up the hosts as Mushfiqur Rahim (64) - dropped early on by Rohit Sharma - shared half-century stands with Liton Das (35) and Mehidy Hasan (38).
Tailender Taijul Islam (6 off 43 balls) hung around, too, but India finally dismissed the Tigers for 213 - Mushfiqur the penultimate man out - to complete a sixth straight Test victory, with seamer Mohammed Shami taking 4-31 and off-spinner Ravichandran Ashwin 3-42.
India have won their last three Test matches by an innings, after also hammering South Africa in Pune and Ranchi in October.
Kohli's side will now secure a record-extending 12th straight Test series win at home if they avoid defeat against Bangladesh in the second and final game of the series, a day-nighter at Eden Gardens in Kolkata from Friday.
Umesh Yadav (2-51) bowled Imrul Kayes (6) on the drive in the sixth over of Bangladesh's second innings - Kayes' miserable match complete after he made only six in his side's opening knock and then dropped Agarwal on 32.
Shadman Islam (6) also matched his first-innings score before he was bowled through the gate by Ishant Sharma (1-31), with Bangladesh sinking to 44-4 before lunch with skipper Mominul Haque (7) and Mohammad Mithun (18) out to Shami - Mominul lbw and Mithun caught.
Shami struck again after the interval as Mahmudullah (15) prodded him to slip but Liton and Mehidy dug in before they were caught and bowled by Ashwin and castled by Umesh respectively.
Taijul stuck with Mushfiqur for almost 12 overs before Shami bounced him out, with Mushfiqur then caught superbly by Cheteshwar Pujara at mid-off off Ashwin and last man Ebadat Hossain (1) skying Ashwin to long-on.
Bangladesh - without star all-rounder Shakib Al Hasan due to his year-long ban for failing to report corrupt approaches as well as batsman Tamim Iqbal for personal reasons - have never beaten India in a Test, losing eight and drawing two of the 10 games between the sides.