Earlier, Brendon McCullum channelled chess grandmaster Garry Kasparov, Williamson aped slip aficionado Mark Taylor and Tom Latham mimicked expert short leg David Boon.
At lunch England were 102 for five with rain scheduled to enter down the order in the early afternoon. The precipitation proved a flaky teammate, seemingly falling everywhere but the ground.
A victory for the visitors would be their second at Headingley, fifth in England across 54 tests and extend their run of undefeated series to seven dating back two years.
Extraordinarily, their ranking will drop from third to fourth regardless. A draw or loss would drop it to seventh.
McCullum marshalled his fielders around the bat like rooks, knights and bishops, particularly for the off-spin of Mark Craig.
Left-hander Gary Ballance was the best example. Two slips, a leg slip and a short leg assumed their positions as Craig zeroed on the footmarks outside off stump. Checkmate loomed.
Ballance eventually went for six from 26 balls when a Trent Boult delivery clipped his pad and cannoned into off stump. Boult also forced Adam Lyth to defend on the back foot outside off to entice the edge.
Craig continued a fine test after struggling with the ball at Lord's. He supplemented two for 48 from 26 overs in the first innings with two for 63 from 28 overs in the second. Those figures included seven maidens and 15 consecutive overs from the Kirkstall Lane end in the opening session, as his responsibility grew.
The territory is nothing new. Craig has bowled New Zealand to victory in three of his previous nine tests; on debut against the West Indies in Kingston, against Sri Lanka in Wellington and against Pakistan in Sharjah.
The decision to open with Craig was sound. McCullum was looking for him to hit the footmarks outside off stump for England's seven left-handers, and especially Cook, who appeared to have a GPS locator on his off stump to pace bowling across his last three innings.
With England four down, McCullum inserted himself at silly point when Stokes, who blasted the 85-ball fastest century at Lord's, emerged.
The captain was unflinching even when Craig dropped short and the all-rounder's backlift took a deep breath, tipping beyond the horizontal in prospect at drilling shots through McCullum's solar plexus.
The catching of Williamson and Latham provided the other New Zealand highlights.
Williamson showed dexterity taking Ian Bell with two hands, low to his left for one.
Latham's effort at short leg, to remove local hero Joe Root for a duck second ball, was more unorthodox. Root hit the ball into what proved an adhesive sternum. Latham quickly clasped his hands around the gift. The Headingley crowd was silent.
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