Broad (four for 38) and James Anderson put the home reply to 307 all out in big trouble on 36 for five early on the second afternoon, only for Colin de Grandhomme (72) and BJ Watling (77no) to reprise the resistance led 24 hours earlier by England's centurion Jonny Bairstow.
Their record stand of 142 helped New Zealand to 192 for six by stumps - and whatever the remaining twists and turns, they had already ensured no one-way traffic here as they bid for a famous series win and England try to avoid ending their conspicuously unsuccessful winter on another low note.
The tourists' new-ball pair threatened to consign New Zealand to the same dire straits they had chartered themselves on day one of this series in Auckland last week.
Broad struck with just his third delivery, Tom Latham edging an attempted drive to Bairstow for a duck, and the Kiwis were minus both openers when Jeet Raval fell in similar fashion to Anderson.
By the end of the 10th over, it was 17 for four, with Broad apparently kickstarting one of the hot streaks for which he used to be famed.
He had Ross Taylor edging another attempted drive to Alastair Cook at slip, and then overturned an initial not-out verdict against Henry Nicholls - who fell for a duck on his home ground.
Kane Williamson had already had the closest of calls against Anderson when he survived a review for lbw on nine, but he could not make it count after lunch as England's all-time leading wicket-taker got him anyway - with Bairstow's help, catching down the leg-side this time.
That, though, was the high point of the tourists' fortunes before De Grandhomme and Watling shut out everyone for 50 overs - including three from Ben Stokes, his first in a Test since last September thanks to his stiff back of late - in their country's highest sixth-wicket stand against England.
De Grandhomme almost immediately served notice of his intent to counter-attack, as he quickly climbed into three leg-side fours in four balls off Mark Wood - who, unlike his pace colleagues, religiously followed an apparent gameplan to bowl short and fast.
It resulted in one alarming clunk on the head for Watling, on 10, but little else of note other than an occasional mis-hook which missed the field.
As on day one, batting became a relatively serene pursuit against an older ball - and as the Kiwi pair cashed in, de Grandhomme deposited a 75-ball 50.
Watling followed at a more studied tempo from 125, albeit with a slog-swept six off debutant spinner Jack Leach to reach the milestone.
It took the evening return of Broad to at last bring a breakthrough when with only the second delivery of his new spell he had De Grandhomme edging behind as he moved above Curtly Ambrose into 14th in the all-time Test list with 406 wickets.
England's final two wickets had occupied only 6.5 more overs on the morning resumption, in which Bairstow (101) added the three runs he needed for his fifth Test hundred and one more too before he was last out upper-cutting Trent Boult (four for 87) to third-man.
Leach departed two balls later, caught-behind off Tim Southee (six for 62), to end a stand of 48.
England might have hoped to add a few more, but their own recovery from 94 for five was still enough to give them a mid-match edge.