Sohag Gazi became the first player to his Test century and take a hat-trick in the same match to star for Bangladesh despite their first Test with New Zealand ending in a draw.
Rain on the fourth day always meant a draw was likely, but both sides did their best to try and get a result on the final day of play.
The Black Caps declared their second innings on 287-7 in Chittagong to set the hosts a victory target of 256 in a minimum of 45 overs - after 22-year-old Gazi finished with 6-77 and a hat-trick.
Bangladesh made it to 173-3 and within 83 runs of victory but they were never going to have enough time to get there and play was called off with 48-2 overs of their innings played.
Earlier, a 74-run stand from Kane Williamson kept the match drifting steadily towards a draw but, after Gazi dismissed both the Yorkshire batsman and Peter Fulton before lunch, he returned to the crease to wreak havoc.
Brendon McCullum, who would eventually declare on 287 for seven, was first to go before Corey Anderson, BJ Watling and Doug Bracewell fell to successive balls in the 85th over.
Tamim Iqbal and Anamul Haque then contributed 38 runs for Bangladesh before tea at the Zahur Ahmed Chowdhury Stadium.
Iqbal made 46 and Haque added 17, while Marshal Aiyub hit 31before Shakib Al Hasan scored a half-century but it was not enough to get them over the line.
Gazi, who took a late wicket on Saturday, joins team-mate Shakib on the list of players who have both scored a century and taken five wickets in an innings in the same Test match.
Bangladesh did get just their second draw against New Zealand but will try for their first win in the second Test, which will be played in Dhaka on October 21.