India picked up three Bangladesh wickets in the morning session after declaring their first-innings on 462 for six but rain washed out the rest of the fourth day as the one-off Test headed for a draw.
India raised hopes of an unlikely win as spinner Ravichandran Ashwin took two wickets and comeback man Harbhajan Singh another to restrict Bangladesh to 111 for three when bad light forced the players off for an early lunch.
Opener Imrul Kayes was at the crease on 59 with the experienced Shakib Al Hasan yet to open his account.
Left-hander Tamim Iqbal (19) went past former captain Habibul Bashar as Bangladesh's highest run-scorer in Tests before he was stumped by wicketkeeper Wriddhiman Saha off Ashwin.
Kayes added 81 for the second wicket with Mominul Haque (30) to steady the Bangladesh innings before the latter fell to Harbhajan.
Kayes had just got away with a thick edge for a boundary after charging down to Harbhajan, who is playing his first match for India in over two years, but Mominul tried to repeat the shot two deliveries later and was caught.
Ashwin picked up his second wicket in the next over when Bangladesh captain Mushfiqur Rahim (two) got an edge on to his pads that went straight to Rohit Sharma at backward short leg.
India India 462-6d (Dhawan 173, Shakib 4-105)
Bangladesh 111-3 (Kayes 59, 2-30)