His twin strike left New Zealand struggling through to tea on the fourth day at 492 for eight, still 103 runs behind Bangladesh's mammoth 595 for eight declared.
The 30-year-old Mahmudullah had been kept out of the attack for the first 132 overs as New Zealand edged towards wiping out the first innings deficit on the back of a sterling 177 by opener Tom Latham.
With Latham's departure just before lunch it was left to BJ Watling and Mitchell Santner to keep their innings alive.
Watling, who has twice scored crucial centuries at the Basin Reserve in recent years, was on 49 and looking comfortable when he tried to flick away a wayward off-break from Mahmudullah's opening delivery.
Wicketkeeper Imrul Kayes' appeal for a catch down the leg side was initially turned down, but the confident Bangladeshis sought a review which detected the ball had made contact with the bat.
Southee was then struck on the back pad to be leg before wicket as New Zealand slumped to 473 for eight.
New Zealand, who resumed the blustery Wellington day at 292 for three, have lost five wickets in the first two sessions.
Henry Nicholls was first to fall, smartly caught at leg slip by Mehedi Hasan for 53 to snap a 142-run stand with Latham for the fourth wicket.
Colin de Grandhomme, looking to score quickly, reached 14 with a six off Subashis Roy but on the next ball was caught behind to give the 28-year-old his first wicket in his debut Test.
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