India spinners shared eight wickets to help India win by 208 runs. Ishant Sharma picked up two wickets.
India set Bangladesh a target of 459, in reply to which the visitors are 103/3 at stumps on day 4 at Hyderabad on Sunday.
Bangladesh reach 322-6 after Shakib, Mushfiqur and Mehedi hit gritty half-centuries, still trail by 365
India declared their first innings on 687-6 after Kohli posted another double century and Saha also reached three figures.
Vijay and Kohli heped themselves to centuries while Pujara fell for 83 as India ended Day 1 on 356-3.
Bangladesh eye strong showing in first-ever Test in India starting February 9 in Hyderabad.
Kuldeep Yadav was on Tuesday named as a replacement for Amit Mishra for the one-off cricket Test against Bangladesh at Hyderabad.
Bangladesh will now take on India in the one-off Test at Hyderabad, beginning from February 9.
India A in command at stumps on Day 1 after Bangladesh declare at 224-8 in 2-day warm-up match
Bangladesh on Wednesday announced the 15-member squad to take on India from next Thursday.