The World Test champions were dismissed for 132 before England, in the first of this three-match series, slumped to 116-7 by stumps.
Pre-match, there had been talk of England making a fresh start under new Test captain Ben Stokes and recently-appointed red-ball coach Brendon McCullum, the former New Zealand skipper.
But this was a reminder there are no quick solutions to the fundamental batting weakness that has contributed to England winning just one of their previous 17 matches at this level, a run that has left them bottom of the World Test Championship table.
Potts took a superb four wickets for 13 runs in 9.2 overs, a reward for a challenging line and length, with recalled England pace great James Anderson returning figures of four for 66 in 16.
Bowlers dominate on day one 🔴🏴 #ENGvNZ 🇳🇿 | @LV https://t.co/t7pg4XxvO7
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Zak Crawley launched England’s reply with a brisk 43.
But the opener’s exit sparked a slump that saw England lose seven wickets for just 41 runs on a good pitch beneath sunny blue skies — seemingly ideal batting conditions.
Stokes himself was out for just one, with former captain and star batsman Joe Root dismissed for 11.
New Zealand left-arm quick Trent Boult, who only arrived in England on Monday after playing in the Indian Premier League final, took two for 15 in 10 overs and towering paceman Kyle Jamieson two for 20 in seven.
Crawley had looked in superb touch, with the best of his seven fours a straight drive off Tim Southee. But after he was caught behind off Jamieson, wickets tumbled.
Root struck a trademark forcing shot for a four off all-rounder Colin de Grandhomme only to be caught in the gully playing a similar stroke off the same bowler for 11.
“Stokesy asked me, ‘Are you ready to be a Test cricketer’?” 💪@MattyJPotts looks ahead to his Test match debut 🦁… https://t.co/uNaMfS4Hhf
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Alex Lees struggled to make 25 off 77 balls before Stokes was caught behind for just one off Southee.
Jonny Bairstow was also out fot a single before Boult brought Potts back down to earth by removing the newcomer for a duck in his first Test innings — the last of a remarkable 17 wickets that fell in the day’s play.
New Zealand had been in dire straits at 45 for seven after captain Kane Williamson’s decision to bat first.
But all-rounder de Grandhomme’s unbeaten 42 off 50 balls bolstered their total.
Anderson and Stuart Broad, England’s two most successful Test bowlers of all time, with 1,177 wickets between them prior to this match, had both been controversially left out of a 1-0 series loss in the Caribbean earlier this year.
But the 39-year-old Anderson was soon back in a familiar groove as he removed openers Will Young and Tom Latham with the aid of two slip catches, the first a brilliant diving one-handed effort, by Bairstow.
New Zealand’s Devon Conway, who made a double century at Lord’s in his Test debut last year, fell for just three on Thursday when caught by Bairstow off Broad.
England’s Jack Leach had to leave the field half an hour into the day’s play after the spinner landed on his head and neck when stopping a boundary.
Leach was later ruled out of the rest of the match due to symptoms of concussion, with England summoning uncapped Lancashire leg-spinner Matt Parkinson from Manchester as a concussion substitute.
Potts, however, struck with just his fifth ball when Williamson, whose elbow injury meant he had missed New Zealand’s previous five Tests, edged low to wicketkeeper Ben Foakes.