Amid the ruins, Rahim, after getting reprieve in the first session, showed his will to fight that was missing in younger colleague Liton Das (35 off 39 balls), who showed T20 skills when something else was required.
India declared their first innings at 493 for 6 after bowling out Bangladesh for 150 in the visitor's first essay. In their second innings, Bangladesh were bundled out for 213.
India remained on course for a big innings victory after their pacers blew away the Bangladesh top-order, reducing the visitors to 60 for 4 at lunch on the third day of the first Test here on Saturday.
Trafficking often increases after the monsoon, when calm November seas allow small fishing trawlers to travel long distance.
The pace unit, which has been on the top of its game over the last 22 months, bowled a probing line during the first spell and the disconcerting extra bounce made life difficult for the Bangladeshi batsmen.
It could well have been four down but Mushfiqur survived when a thickish outside edge off Umesh's bowling flew towards a diving Kohli's right but the ball popped out of his hands.
Skipper Virat Kohli had his first experience of negotiating a pink ball as Indian cricketers took turns to get used to the new colour during the net session ahead of the first Test against Bangladesh, starting Thursday.
"I think every player faces such a time when in four, five or six matches, you can't perform as your team expects. We all know that he is a champion bowler and sometimes as a team we expect more from him."