Tom Latham shouldered arms on four to allow a Jimmy Anderson a free shot at the stumps after a boomerang of a Duke ball was plucked from the umpire's box.
A Devon Conway sweep off Jack Leach caught a top edge, bringing Jonny Bairstow onto the radar at deep square leg. He exited for 52 after a stabilising century partnership with Will Young.
Henry Nicholls survived an appeal for a slip catch after reverse-sweeping Jack Leach second ball. He then scythed Matthew Potts into the Venus fly-trap hands of Alex Lees at backward point on three.
Young then mimicked the crossing of a London intersection at rush hour after pushing into the legside. Ollie Pope and Ben Stokes combined for an alley-oop on the stumps to dismiss him run out for 56.
Mitchell and Tom Blundell built what has become a bricks-and-mortar recovery of late to move New Zealand from 131 for four to 176 for five when Blundell hooked Stuart Broad into the hands of Ben Stokes at short fine leg.
Michael Bracewell also clubbed a handy 25.
The pace of the match means any result remains plausible. World championship points should provide an incentive to avoid the draw.
New Zealand's best chance appears to be batting on the surface for another 60 to 90 minutes before presenting a chase.
England need wickets and the positive intent they applied successfully in the fourth innings at Lord's.
Earlier, Trent Boult and Trent Bridge continued on their path towards becoming best friends forever or "BFFs" to use the modern parlance.
The New Zealand left-armer took five wickets for 106 runs from 33.3 overs to help dismiss England for 539 on the fourth day of the second test.
He has never previously played at the ground.
Boult's return marks his 10th five-wicket bag from 77 matches, and fifth against England.
New Zealand's Daryl Mitchell, right, plays a shot during the fourth day of the second test. Photo / AP
The day started with a flurry. England scored 43 runs from the first five overs before a slower ball from Boult lured Joe Root (176) to popping a catch to Tim Southee at cover. The hosts' last four wickets fell for 12 runs in 35 balls.
Ben Foakes (56) was the victim of a run out mix-up with Matthew Potts. Nicholls' bullet throw from mid-wicket offered no room for hesitation.
A clinical and straight-forward operation unfolded from there. Mitchell extended a right mitt at first slip which allowed Bracewell to claim Broad, Boult bowled Potts, and Tom Blundell stumped Anderson for Bracewell's third. The off-spinner finished with three for 62 from 17.2 overs in a compelling display from a supposed part-timer.
Pace bowler Kyle Jamieson did not take the field as he awaits word on the damage to his lower back.
He had an MRI scan after the previous day's play to determine the extent of the injury. Jamieson exited late on the third day after experiencing sharp pain while bowling in the final session.
