England had earlier ridden half centuries from Joe Root, Harry Brook and Ben Foakes to reach 374 all out in their second innings and set the Black Caps a mammoth 394 to win.
Seamer Broad (4-21) drove home the advantage in stunning fashion by bowling Devon Conway, Kane Williamson and Tom Latham through the gate in short order before returning to remove first innings centurion Tom Blundell for 15 in the same style.
Ollie Robinson chipped in with the wicket of Henry Nicholls for seven and Daryl Mitchell (13 not out) and Michael Bracewell (25 not out) will resume on Sunday with two days of the match stretching out in front of them.
“It’s just a different pitch to bowl with in the lights,” Broad told reporters. “It nips pretty quickly under lights and I found a really good rhythm. Once I got Conway, I felt it could really be my day. Hopefully we can have a good first hour tomorrow and get moving.”
The tourists had started the day on 79-2 but were soon unleashing another onslaught of “Bazball” cricket on their hosts under sunny skies in Tauranga. Quick Neil Wagner (2-110) came in for particular punishment in the opening session as first Ollie Pope (49) and then Brook (54) flayed his bowling with a flurry of sixes and fours and England added 158 runs to their overnight tally.
Root looked less comfortable with the attacking style but worked his way neatly to 57 before an ill-judged attempt at a reverse sweep resulted in a top edge which was caught in the slips off the wicketkeeper’s gloves.
That brought up the first break and on the resumption Foakes and his skipper Ben Stokes, perhaps fearing England were getting too far ahead of the game, slowed the pace of the attack.
The England skipper’s 31 included his 108th six to take him past his coach Brendon “Baz” McCullum as the most prolific scorer of the maximum in Test cricket history.
Wagner could have dismissed him on the next delivery but his miserable day continued when he caught the England skipper on the boundary only to fall over the rope and give Stokes his 109th Test match six.
SCOREBOARD
England 1st innings 325-9 declaredNew Zealand 1st innings 306
England 2nd innings (overnight 79-2)
Z. Crawley c Blundell b Kuggeleijn 28
B. Duckett c Latham b Tickner 25
O. Pope c Blundell b Wagner 49
S. Broad c Nicholls b Wagner 7
J. Root c Mitchell b Bracewell 57
H. Brook c Mitchell b Tickner 54
B. Foakes c Blundell b Tickner 51
B. Stokes st Blundell b Bracewell 31
O. Robinson c Nicholls b Kuggeleijn 39
J. Leach st Blundell b Bracewell 12
J. Anderson not out 6
Extras (b5, lb6, nb2, w2) 15
Total (73.5 overs) 374
Fall of wickets: 1-52 (Duckett), 2-68 (Crawley), 3-82 (Broad), 4-144 (Pope), 5-225 (Brook), 6-237 (Root), 7-293 (Stokes), 8-335 (Foakes), 9-358 (Robinson), 10-374 (Leach)
Bowling: Southee 15-2-49-0, Wagner 13-0-110-2 (1nb), Tickner 12-0-55-3 (1nb), Kuggeleijn 14-1-81-2 (2w), Bracewell 19.5-2-68-3
New Zealand 2nd innings
T. Latham b Broad 15
D. Conway b Broad 2
K. Williamson b Broad 0
H. Nicholls c Foakes b Robinson 7
D. Mitchell not out 13
T. Blundell b Broad 1
M. Bracewell not out 25
Extras 0
Total (5 wkts, 23 overs) 63
Fall of wickets: 1-14 (Conway), 2-14 (Williamson), 3-19 (Latham), 4-27 (Nicholls), 5-28 (Blundell)
Bowling: Anderson 3-1-3-0, Broad 10-5-21-4, Robinson 8-0-34-1, Leach 1-0-5-0, Root 1-1-0-0