Tom Blundell made 90 and was the last man out as New Zealand’s second innings ended at 483 less than an hour before stumps.
It means England have now won 10 of their most recent 11 Test matches, with their only blemish since McCullum took over as coach early last year coming at the hands of South Africa at Lord's.
Stuart Broad and James Anderson made history by claiming the record for most Test wickets as teammates from Australian greats Shane Warne and Glenn McGrath.
England vs New Zealand, T20 World Cup 2022 Highlights : Phillips Fifty In Vain As ENG Beat NZ By 20 Runs.
Williamson has led New Zealand to 21 wins and nine losses across 36 Test matches since becoming the skipper of the side.
Anderson and Broad make a return to the Test squad after featuring in the 2021/22 Ashes in Australia before being surprisingly left out of three-match away tour to West Indies in March.
Wood, who got into the playing eleven at the expense of Mills in the last match of Super 12 against South Africa and semi-final against England, feels that England not winning the ongoing tournament is a missed opportunity.
Neesham scored an important 11 ball 27, which included three maximums and a solitary boundary striking at a rate of 245.5.
Neesham played an important knock off 27 off 11 deliveries with Man of the Match Daryll Mitchell before he was sent back to the pavilion by England spinner, Adil Rashid.
Morgan said England were devastated after losing a thrilling and desperately close T20 World Cup semifinal to a New Zealand side.