Ollie Robinson marked his England bow with two for 50 but the opening day of the first Test belonged to South Africa-born Conway, who was preferred to Tom Blundell and Will Young as Tom Latham’s opening partner.
He rewarded the decision with a series of punchy drives and stout defence in a self-assured 136 not out, becoming the sixth batsman to make a debut hundred at the Home of Cricket, as the tourists reached 246 for three at stumps.
James Anderson dismissed Kane Williamson for the seventh time - the most success any bowler has had against the Kiwi captain - but it was a rare moment of joy for the Lancastrian as he equalled the record for most England caps.
Robinson was spirited after being preferred to Craig Overton but there was no room for a specialist spinner in England’s XI on a day where the hosts played in front of a home crowd for the first time since the summer of 2019.
They worked themselves into a position of promise after New Zealand slipped to 114 for three in mid-afternoon but Conway and Henry Nicholls (46no) put on an unbroken 132-run stand to subdue Joe Root’s side.
Unlike New Zealand’s last visit to St John’s Wood - when they were beaten by England on boundary countback alone in a dramatic 2019 World Cup final - there were few fireworks at the start of this two-match series.
The Black Caps have, though, laid the foundations to go big in their first innings even if England are unlikely to be too downcast after their attack put in a wholehearted effort on a pitch that offered them very little.
Robinson was able to exploit a fraction of movement to bowl Latham via the inside edge then trap Ross Taylor lbw, but while New Zealand were never really able to accelerate at any point, there seemed to be no demons in the track.
Conway, who qualified to represent New Zealand last August, has made an impressive start to life as an international cricketer, averaging 75 from three one-day internationals and 59.12 from 14 Twenty20s.
He was thrust into action immediately after New Zealand won the toss under sunny skies but he had to wait until the start of the fourth over to face a ball as Latham farmed the strike against Anderson and Stuart Broad.
Conway settled into his stride with crisp drives off Broad, standing in as vice-captain in the absence of the injured Ben Stokes, then Anderson as New Zealand’s openers looked untroubled in a half-century opening stand.
Robinson, one of two England debutants alongside wicketkeeper-batsman James Bracey, overstepped with his first delivery in international cricket but showed no hint of nerves thereafter as he plugged away on a length.
After casting some doubt in Latham’s mind with one that moved away, the Sussex seamer made the breakthrough with one that came back in slightly, the left-hander getting neither forward nor back and bowled via an inside edge.
Mark Wood drew gasps from the crowd - capped at 25 per cent for the next few days - by cranking up the pace on his introduction, regularly reaching the mid-90mph range, with Conway twice rapped on the arm just before lunch.
England had their second wicket four balls after lunch when Williamson, on 13, dabbed an innocuous Anderson delivery on to his stumps while Robinson trapped Taylor in front for 14 after the veteran played across the line.
But Conway and Nicholls steadied New Zealand either side of tea by blunting England’s bowlers.
In the first hour of the final session of the day, Conway crowned an unforgettable day by reaching three figures with an audacious flick off Robinson for his 11th four.
Root sent down 12 overs of his part-time off-spin and, while England took the second new ball shortly before the close, they were unable to make any further inroads as New Zealand ended the day on top.