Aaron Redmond scored a maiden Test half century as New Zealand made a solid start after being set a victory target of 317 by Bangladesh in Chittagong.
Redmond made an unbeaten 62 out of a total of 145-2 and shared stands of 55 and 90 with Jamie How and Jesse Ryder.
Their position would have been even stronger had Ryder not been needlessly run out for 38 shortly before stumps.
Redmond earlier took the vital wicket of Mashrafe Mortaza for 44 as the home side were all out for 242.
It was the 29-year-old's first success with the ball in Test cricket and the day got even better from then on as he laid the foundation for New Zealand's run chase.
606: DEBATE
Bangladesh managed to add 58 to their overnight 184-8 during the morning session, thanks mainly to a 40-run partnership between Mortaza and Razzak.
It was ended when Razzak edged a ball from Iain O'Brien to Ross Taylor at slip and Mortaza followed when he attempted a big hit off Redmond's leg-spin and was stumped by Brendon McCullum.
Facing a tough target, the New Zealand openers avoided unnecessary risks and were content to bid their time and try to pick off anything loose.
How pulled a short ball from Mortaza for six and also collected five boundaries, but paid the price for trying to cut a turning ball from Razzak.
Redmond was undisturbed by his partner's downfall, however, and passed fifty with two successive fours off paceman Shahadat Hossain.
The powerful Ryder was in restrained mood after managing only a single in the first innings.
And it looked like he and Redmond would see things through to the close when he dabbed a ball down to third man and was beaten by Mortaza's throw as he attempted a second run.
It was exactly the lift Bangladesh needed and Razzak insisted: "We are still in the game. The pitch has variable bounce, but the spin is slow.
"They still need more than they got in the first innings - and we need eight wickets."
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