New Zealand's Conway makes debut double century before England collapse
Conway was last man out in a first-innings total of 378 on the second day of this two-match series.
The South Africa-born left-hander was in sight of becoming the very first batsman in the 144-year history of Test cricket to carry their bat -- bat throughout the entire innings -- in their first knock in the format when he was run out to end a stay of more than nine-and-a-half hours.
Nevertheless, it needed a review of a close call before it was confirmed that England captain Joe Root had taken the bails off in time.
He faced 347 balls, with 22 fours and went to 200 in style when he hooked fast bowler Mark Wood for the only six of his innings.
New Zealand No 11 Neil Wagner, also born in South Africa, made 25 not out off 21 balls that included a superb straight six off Stuart Broad during an entertaining last-wicket stand of 40.
But New Zealand, who face India in the inaugural World Test Championship final at Southampton later this month, then struck twice with the ball themselves.
Towering paceman Kyle Jamieson had Dom Sibley lbw for a duck with a ball that straightened to hit the opener on the back pad, the decision upheld on 'umpire's call' after a review.
But there was no room for doubt when Zak Crawley was caught behind off Tim Southee for two.
At tea, Rory Burns was 15 not out and star batsman Root unbeaten on seven, with England 353 runs behind.
New Zealand resumed on 246-3, with Conway 136 not out after Black Caps skipper Kane Williamson had won the toss.
But they lost four wickets for just six runs as they slumped from 288-3 to 294-7.
Conway shared a fourth-wicket stand of 174 with Henry Nicholls before his fellow left-hander was caught holed out to long leg off Wood for 61 by England debutant Ollie Robinson to spark the collapse
It was a welcome moment for Robinson, who found himself having to apologise after play on Wednesday when racist and sexist tweets he had first posted as a teenager were published again.
Wood then removed BJ Watling for just one, with the aid of a sharp slip catch by Sibley.
Fellow seamer Robinson, who took two wickets on Wednesday, then had Colin de Grandhomme lbw for nought on review, with Mitchell Santner also out for a duck when he chipped Wood to mid-off.
Robinson, however, was deprived of a place on the Lord's honours board when Broad dropped Southee at mid-off to deny him a fifth wicket.