Lunch New Zealand 209 (Southee 73, Broad 4-61) and 40 for 0 (Latham 27*, Conway 13*) trail England 435 for 8 dec by 186 runs
Conway was particularly dogged in crabbing along to 13 off 44 balls, with Robinson troubling him around off stump and short leg interested when he looked to close the face. Tom Latham found a steady rhythm, picking off three boundaries and looking the more secure of the two to reach the break on 27 from 70.
England's bowlers had taken some punishment from Southee on the way to knocking over the final three wickets, enabling them to enforce the follow-on midway through the morning session.
New Zealand's first innings had an anaemic look at 138 for 7 at the close on day two, but they still had a chance of taking the decision out of England's hands with Southee resuming alongside Tom Blundell. Southee duly showcased his six-hitter's eye on the way to a bruising 73 off 49 balls - four runs short of equalling his Test best score, made against England on debut in 2008 - before Broad finished the innings with 3 for 5 in the space of 12 balls.
The best route out of trouble, in Southee's view, was to give free rein to his natural instincts. After Blundell had edged just short of slip in Robinson's first over of the morning, Southee charged at his second ball from Leach and just about got away with a toe-ended slog that cleared Stokes running back from mid-on.
Another full-blooded mow down the ground brought four more in the same over, before Robinson was slapped through the covers. Leach then felt the full force of Southee's world-class ability to hit sixes, three times going the journey in a single over as New Zealand's No. 9 raced to a 39-ball half-century.
Blundell still had designs on averting the prospect of the follow-on, but miscued an advance in Broad's next over to be held by Leach at mid-on. Henry then spliced a catch to backward point to give Stokes the option, which he duly took.