But he removed Burns and the luckless James Bracey, out for a first-ball nought to follow his England debut duck at Lord’s, with successive deliveries in a return of 2-60 in 23 overs.
“It’s been quite a tough day, but it was pretty even by the end,” Burns told Sky Sports.
“Dan played really well and got us back in it nicely,” he added.
“They came back hard at us after lunch. It swung a bit more, whether that was conditions overhead or the surface, we’ll have to see when we bowl.”
Matt Henry had done the early damage as England, who had been 72-0, lost three wickets for 13 runs shortly after lunch, with captain Joe Root out for just four.
Henry, in for the rested Tim Southee ahead of New Zealand’s World Test Championship final against India at Southampton next week, started the slump when he had Dom Sibley caught behind off an away-swinger for 35.
“I think we’re very pleased,” Henry, who ended the day with 2-66 from 22 overs, told reporters.
England’s 72-1 became 73-2 as Zak Crawley’s miserable form continued when he was caught in the slips for a duck off left-arm paceman Neil Wagner -- the only surviving member of New Zealand’s attack from Lord’s.
It was Crawley’s ninth single-figure score in 11 Test innings since his stunning 267 against Pakistan last year.
Henry then captured the prize wicket of Root, caught behind off a late-moving outswinger.
“It’s always great to get big wickets like Joe,” said Henry, who paid tribute to the spectators by saying: “The crowd were fantastic, the Hollies Stand was just electric all day. They were phenomenal and you could see the excitement of everyone getting back into cricket and stadiums.”
Root had won the toss and batted despite overcast conditions that appeared to favour an England attack, again without a specialist spinner and once more missing injured all-rounder Ben Stokes and the rested Jos Buttler, Jonny Bairstow and Chris Woakes.
New Zealand had to make three injury-enforced changes, with captain and key batsman Kane Williamson (elbow), spinner Mitchell Santner (cut finger) and BJ Watling (sore back) all missing.
Their places were taken by Will Young, Ajaz Patel and Tom Blundell respectively, with Tom Latham captaining the team.
Boult struck when Burns, eyeing three figures again after his hundred at Lord’s, drove at an away-swinger and was well caught by Latham in the slips.
The Surrey left-hander faced 187 balls, including 10 fours.
Burns’s exit came off the last ball of the 59th over and the first of the 61st saw Boult tempt Bracey into driving at another outswinger, with Daryl Mitchell -- the son of former All Blacks coach John Mitchell -- holding an excellent catch at third slip.
Lawrence hit several stylish drives while compiling a 75-ball fifty including eight fours.
Meanwhile, James Anderson’s 162nd appearance saw him become England’s most-capped Test player, breaking the record he had shared with retired former captain Alastair Cook.
Stone replaced Ollie Robinson who, following a successful on-field Test debut at Lord’s, was suspended from international cricket after the emergence of historic racist and sexist Twitter posts.