The tourists’ slim hopes of forcing a result lay with forcing the hosts to follow on but the Tigers got past the target of 163 safely, albeit with nine wickets down.
From then on the match was effectively over with only hope for a result being a calamitous batting display second time around from the BLACKCAPS.
But that was not to be despite the early loss of Jamie How (8) who failed to latch on to a pull shot and spooned a ball from Mashrafe Mortaza and was caught by Abdur Razzak at mid on.
However, Aaron Redmond (30 not out) and Jesse Ryder (39 not out) ensured that was not the case to finish on 79-1 when the tedium was brought to a premature end.
Bangladesh had earlier declared on 169 for nine, in reply to the BLACKCAPS’ first innings total of 262 for six declared, after resuming on a precarious 13 for three.
Bangladesh had to overcome a fine bowling display from opposing skipper Daniel Vettori to narrowly avoid being forced to follow on.
Spinner Vettori finished with figures of 5-66, his 19th five-wicket haul in tests, and Iain O'Brien chipped in with three victims for 31 as Bangladesh limped past the target.
All-rounder Skahib Al Hasan (49) and Mashrafe Mortaza (48) provided the bulk of the runs for the home side and shared in a 78-run stand for the seventh wicket to see the Tigers to safety.
Earlier, spinner Jeetan Patel secured the day's first breakthrough, trapping Mehrab Hossain (7) leg before wicket, Vettori got rid of opener Tamim Iqbal and pace bowler O'Brien had Mushfiqur Rahim (7) caught behind by BrendonMcCullum.
After lunch the hosts adopted an aggressive approach to add 65 runs in 10.1 overs but Vettori denied Shakib a test fifty by trapping him leg before to give the spinner his fifth victim. Mortaza adopted the long handle but he had a reprieve when the third umpire ruled a catch had not carried to Ryder in the gully.
The unlucky bowler was O’Brien, but he eventually got his man when Daniel Flynn held a chance in at short leg and he also claimed Shahadat Hossain cheaply to force the declaration.
Vettori was named man of the match and man of the series.