At stumps, England were 180 for six in their second innings -- a lead of 205 runs.
England were building a sound position at 159 for two when paceman Southee wrested back the initiative with three wickets for four runs in 17 balls.
In all, England lost four wickets for 12 runs to throw the first of this two-Test series wide open, although their lead was now almost as much as New Zealand's meagre first innings 207.
"Now we're into the bowlers," Southee, who had close of play figures of three for 34 in 14 overs, told reporters.
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"Finn is in and we know (Stuart) Broad is capable with the bat and (Graeme) Swann is dangerous, he can score some quick runs. We can't get too far ahead of ourselves. We've still got a job to do."
Jonathan Trott (56) and Joe Root (71) shared a third-wicket stand of 123 before the latter's exit sparked England's slump.
They had steadied the ship after England captain Alastair Cook and fellow opener Nick Compton had fallen to the left-arm pace duo of Trent Boult and Neil Wagner respectively with the score on 36.
A direct hit by New Zealand captain Brendon McCullum would have seen the Yorkshireman run out but Root just did enough as wicket-keeper BJ Watling tried to make the best of a bad return with a despairing effort of his own.
Watling injured his knee in the process and was replaced behind the stumps by McCullum, who had given up keeping in Tests because of knee and back problems.