Ashraful scored an impressive 67 under pressure as Bangladesh recovered from 5-3 to reach 165-6 at stumps after choosing to bat on a slow, turning wicket at the Bangabandhu National Stadium on Tuesday.
Khaled Mashud, leading in the absence of injured captain Habibul Bashar, was on 12 with Manjural Rana on 16.
Bangladesh lost three wickets in the opening seven overs against a disciplined New Zealand pace attack before Ashraful steadied the innings with a 115-run stand for the fourth wicket with Rajen Saleh (41).
Fast bowler Jacob Oram did the early damage, claiming two quick wickets in his lively opening spell to put the hosts in trouble. Left-arm seamer James Franklin also chipped in one wicket to finish the day with 2-23.
Ashraful and Saleh then batted sensibly against both pace and spin to deny the tourists success for more than three hours.
Saleh fell in the closing overs of the afternoon session, slashing Franklin to gully where Oram held a splendid catch. He struck one six and five fours.
Left-arm spinner Daniel Vettori struck twice in the closing session to end a Bangladeshi fightback, removing Ashraful and Alok Kapali. He was the most difficult bowler to get away, conceding just 26 runs off 29 economical overs.
Ashraful kept the New Zealand attack at bay before losing his patience and wicket. He attempted a big shot off Vettori, only to be caught by Nathan Astle in the deep.
"It was a bad decision to go for such a shot," said Ashraful.
"I just tried to play my natural game. I just wanted to stay at the crease. I think a score of 250 will be good on this slow pitch."
Ashraful was the most aggressive batsman, reaching his fifth Test half-century with a six over square-leg off spinner Paul Wiseman. He hit three sixes and eight fours.
New Zealand dominated the morning session as Oram struck twice and Franklin once. The hosts could score only 38 in 29 overs.
Their problems began in the first over when Oram had opener Hannan Sarkar caught by skipper Stephen Fleming at first slip with his third delivery, one that moved away after pitching on the off-stump.
Franklin then bowled Javed Omar, who inside-edged an attempted yorker on to his stumps.
Nafis Iqbal made a forgettable Test debut when he edged Oram to wicketkeeper Brendon McCullum after contributing just one run.
Ashraful and Saleh then propped up the innings with their timely century stand.