Zimbabwe closed day four at the Queens Sports Club in desperate trouble on 58 for three after New Zealand had smashed a quick-fire 166 for two declared in 36 overs in their second innings.
Craig Ervine and nightwatchman Donald Tiripano will resume in the morning having yet to get off the mark after Zimbabwe lost their top three before the close.
Chamu Chibhabha (21) edged seamer Neil Wagner to Martin Guptill at third slip before Tino Mawoyo (35) was trapped lbw by Boult in the penultimate over.
It got worse for the hosts when two balls later Southee produced a superb in-swinger to have Sikandar Raza (0) leg before as well.
Survival will be top of the agenda for Zimbabwe on an excellent batting wicket but they must find a way to counter the prodigious swing of the New Zealand seamers.
Zimbabwe were 305 for six overnight in their first innings and lost their remaining four wickets for 57, including anchor Ervine for 146, his maiden test century, as he picked out Wagner at long-off off the bowling of spinner Ish Sodhi.
The latter was the pick of the visitors’ attack with 4-60 as New Zealand chose not to enforce the follow-on having been in the field for 143.4 overs.
They rather pushed for quick runs in their second innings but slipped to 26 for two before captain Kane Williamson (67 not out) and Ross Taylor (68 not out) shared an unbeaten third wicket-wicket stand of 140.
The declaration came four overs after tea, leaving the tourists a minimum of 116 overs to bowl out their hosts.
New Zealand lead the two-match series 1-0 after an innings and 117-run victory in the first test.
(Reporting by Nick Said, editing by Ed Osmond)
