The visitors, who began their second innings 250 runs behind New Zealand after dismissing them for 393 earlier in the day at the Basin Reserve, crumbled to 51 for five in their second innings, still 199 runs away from making New Zealand bat again.
Habibul Bashar was on 21, while all rounder Shakib Al Hasan was with him on four.
Bangladesh will be further hampered on Monday by the knowledge that recognised opener Tamim Iqbal has a broken thumb after dropping a catch on Sunday and may not be able to bat at all in their second innings.
New Zealand won the first Test in Dunedin by nine wickets within three days.
After New Zealand's Daniel Vettori (94) and Stephen Fleming (87) both fell agonisingly short of making hundreds in New Zealand's first innings, the bowlers rammed home the advantage by striking at regular intervals.
DESPERATE TROUBLE
Kyle Mills had Junaid Siddique caught behind by Brendon McCullum for two when he mistimed a hook and the ball feathered his glove, before makeshift opener Shariar Nafees nicked to Matthew Bell in the slips off Chris Martin in the next over.
Captain Mohammad Ashraful then mistimed a drive off a full delivery from Mills and the ball flew to Fleming at first slip to leave Bangladesh in deep trouble at 30 for three.
Bashar and Aftab Ahmed then attempted to halt the slide with a defensive mindset before a full delivery from Iain O'Brien just shaped away and Ahmed's knick went through to Fleming.
Mushfiqur Rahim also struggled and when he was caught behind by Bell off Oram for a duck the visitors were in desperate trouble at 45 for five.
New Zealand's innings had been anchored by Vettori, who struck 17 boundaries in an 87-ball innings but missed out on a third Test century when he was caught and bowled by Aftab.
Fleming had a life on 61 when he was dropped by Shariar Nafees at deep mid-on but his luck ran out after lunch when he was caught at deep mid-wicket by Aftab off Shakib Al Hasan after an innings featuring 13 boundaries.
(Reporting by Greg Stutchbury in Melbourne; Editing by Peter Rutherford)
