Bangladesh need just 40 runs to create history at the Bay Oval in Mount Maunganui as they limited New Zealand's lead to only 39 in their second innings.
The hosts could not add more than 22 runs to the overnight total and it took Ebadot Hossain and co just 10.4 overs to take the remaining five New Zealand wickets.
Ebadot Hossain and Taskin Ahmed got the ball to reverse right from the beginning of the final day and immediately got their rewards. Ebadot struck in just the second delivery he bowled on the final day. He sent back Ross Taylor, unbeaten overnight on a chancey 37, and became the first Bangladeshi pacer to register a five-for in Tests since 2013. Ebadot also became the second bowler after Rubel Hossain to pick up a five-wicket haul in New Zealand.
There was no stopping Ebadot. He got rid of Jamieson before he could trouble the scorers. Shoriful Islam took a sensational catch at short midwicket to help Ebadot register the best bowling figures in New Zealand by a Bangladeshi bowler.
The hosts were eight down in the very next over as Rachin Ravindra, their last recognised batter, nicked one to Liton. The fast bowler removed Tim Southee in his next over with a full and straight delivery and the lead was only 31 by then.
Trent Boult, the New Zealand number 11, hit two boundaries in consecutive deliveries off Taskin to stretch the lead to 39. A couple of overs later, Mominul brought in Mehidy Hasan Miraz and that immediately paid dividends. He got the better of the aggressive Boult as Taijul Islam, the substitute fielder, took a brilliant catch.