New Zealand skipper Tom Latham enforced the follow-on and the visitors were 395 runs behind when they started batting in their second innings.
Bangladesh could not make hay despite perfect batting conditions on day three in Christchurch as half of their batters went back to the pavilion before the tea break. Three of those wickets were taken by Neil Wagner who bowled a barrage of short-pitch deliveries to trouble the batters. However, Liton Das negotiated Wagner well and was undefeated on 23. Nurul Hasan was not out on six. At tea, Bangladesh were 152 for five, still trailing by 243 runs.
There were good starts from each of the top four batters but none of them could not go on and make a big one.
The start was pretty assured from the Bangladesh openers - Shadman Islam and Mohammad Naim - as they looked to blunt the new ball without worrying much about scoring. Trent Boult and Tim Southee bowled decently on a surface that had browned up and looked a perfect one for batting.
The seam and extra bounce were always there but the openers got through the opening spell of Boult and Southee without losing a wicket. They left balls and focused on spending time in the middle. Shadman, in particular, got a few scoring opportunities and made good use of them.
But right before the drinks break of the morning session, he was out caught behind down the leg side in an unfortunate fashion. Tom Blundell, the keeper, pulled off a one-handed stunner and Kyle Jamieson accounted for the wicket. Shadman scored 21 off 48 balls and was looking good until the dismissal.
Najmul Hossain Shanto, who came in at three, was dropped on four by Daryl Mitchell at third slip off Jamieson.
Neil Wagner bowled a barrage of short balls in the final half an hour of the first session but Shanto took him on in the 23rd over by hitting a six and a four in successive deliveries. The southpaw once again went after Wagner in his next over, hitting back-to-back boundaries off pull shots. But Wagner had the last laugh as Shanto opted for a suicidal pull shot and this time it went straight to Boult at fine leg just minutes before lunch.
But Naim showed great resilience and grit to consume balls before the break without showing signs of getting out. He consumed 81 balls for his unbeaten 15 before the lunch break and Bangladesh went into lunch at 74 for two.
New Zealand got their first breakthrough of the post-lunch session courtesy of Tim Southee and Tom Latham. Naim, who looked good for his 98-ball-24, was caught spectacularly at slip by Latham. Bangladesh were 105 for three then.
Liton Das was given out caught behind on the field but he made good use of the DRS. TV replays showed that the ball brushed his right arm and the decision was reversed. But four balls later, Mominul Haque threw his hand at a delivery pitched way outside off and Ross Taylor took an easy catch. He made 37.
Yasir Ali fell victim to a fired up Wagner not long after Mominul's departure. A typical short delivery from Wagner hit the shoulder of Yasir's bat and Latham took the catch. His dismissal left Bangladesh in all sorts of trouble at 128 for five.
Nurul Hasan stuck together with Liton and got through to the tea break.