The tourists were inspired by Stokes’ Durham team-mate Brydon Carse, whose 10-106 was the first 10-wicket haul in an overseas Test by an England seamer since 2008.
Earlier this year Carse received a three-month ban for historical betting offences, and turned to Stokes for advice.
Asked about the support he received, Carse replied: “Amazing. Over the past four or five months he’s been there, in person or over the phone. I cannot thank him enough.”
Stokes said: “He knows how much value I have in him as a player. I guess it might make him run in a little bit harder every now and again when it’s me asking him to bowl an extra over.
“For him to be where he is now, considering where he was six months ago, is testament to his character.
“You can see why we think of him so highly, that he can go through something like that then be here walking off with 10 wickets in a Test match.”
After Carse’s wickets left England a target of 104, 21-year-old debutant Jacob Bethell crashed his maiden half-century from 37 balls, including the winning runs.
Bethell was batting at number three in this match for the first time in his first-class career.
In the first innings he made 10, but did not look out of place against some high-class New Zealand bowling.
Stokes said: “The second-innings knock was pretty special to watch.
“He didn’t get the runs he would have liked in that first innings, but the way in which he held himself throughout that whole knock… If he sticks to that attitude he will go a long way.”
Bethell occupied the place of regular number three Ollie Pope, who slid to number six because he was keeping wicket after an injury to Jordan Cox. Pope made 77 and had a tidy game behind the stumps.
Durham’s Ollie Robinson has joined the England squad as another keeping option.
Asked if Pope would keep the gloves for the remainder of the series, Stokes said: “We found ourselves with a problem and we solved it.
“That was the make-up of the team for this game and we’ll see in Wellington.”