Only 30.1 overs could be squeezed in the opening session when bad light stopped play with Imrul Kayes (59 batting) and Shakib Al Hasan (0 batting) at the crease.
Earlier, India declared their first innings on the overnight total of 462/6. Bangladesh still trail by 351 runs but look set to sneak away with a draw thanks to weather gods.
Facing the pace-spin combination of Ishant Sharma and Ravichandran Ashwin (2-30), opener Tamim Iqbal (19) became Bangladesh's highest Test run-getter but soon fell to the guile of the wily off-spinner.
Surpassing former batsman Habibul Bashar (3026 in 50 Tests) to manage 3039 runs in 40 matches, Tamim was stumped while trying to counter Ashwin's spin. The left-hander's toe was on the line and the third umpire pushed the red button to send him back to the pavillion.
Kayes though was dropped on 10 when Shikhar Dhawan failed to latch on to the flying cherry on his left side as a dejected Umesh Yadav looked on.
Even a brief rain interruption in the 13th over did not spoil the concentration of the left-handed duo as Virat Kohli continued to juggle his regular bowling options.