Bangladesh were all out for 231 in their second innings on Saturday, setting India a victory target of 145 in the second Test in Mirpur.
Litton Das (73) and Zakir Hasan (51) struck half-centuries for the hosts, who had conceded a first-innings lead of 87 at the Shrere Bangla National Stadium.
Left-arm spinner Axar Patel (3-68) was the pick of the Indian bowlers on day three of the low-scoring contest, reports Reuters.
India are 1-0 ahead in the two-Test series following their 188-run victory in Chattogram on Sunday.
