England took an early lead, but the Kiwis hit back with two tries of their own before Jake Connor’s penalty try on the stroke of half-time sent the teams in level at the break.
New Zealand twice went ahead after the break, but England’s third try, with 13 minutes left, proved decisive.
Inside three minutes England went ahead when Tommy Makinson grabbed George Williams’ kick, surged towards the line and got an offload away.
Elliott Whitehead and Jonny Lomax kept the ball alive and the latter’s pass was finished off by Sam Tomkins, Hull man Connor adding the extras.
On 12 minutes the Kiwis were level when Kodi Nikorima and Shaun Johnson carved out a try for Esan Marsters and Johnson converted.
Jordan Rapana then had a touchdown ruled out by video referee Ben Thaler, after man in the middle Robert Hicks had originally indicated a try.
Eight minutes before the interval Huddersfield winger Jermaine McGillvary knocked on and from the scrum Brandon Smith and Nikorima combined to send Dallin Watene-Zelezniak over.
Johnson converted, but with 53 seconds left in the half Connor slid over from Whitehead’s pass. Hicks indicated a try, but Thaler ruled Connor had been fouled by Watene-Zellezniak preventing him getting the ball down.
A penalty try was awarded and - rather than having a kick from the touchline - Connor squared the scores at 12-12 from in front of the posts.
Johnson and Connor exchanged penalties in the first 13 minutes of the second half, but the Kiwis went ahead for the third time with 19 minutes remaining, Johnson booting hids fourth goal after England had been caught offside defending a kick.
England hit the front with a stunning try six minutes later, Oliver Gildart bursting past the New Zealand full-back from John Bateman’s offload on half-way, though Connor’s conversion attempt from wide out was just off target.
That made it 18-16 and some strong defence in the closing stages sent England into the second Test, at Liverpool on November 4, with a series lead.