The tourists were inspired by Stokes' Durham teammate 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 historic betting offenses and turned to Stokes for advice.
When asked about the support he received, Carse replied: “Amazing. For the last four or five months he has been there for him in person or by phone. I can’t thank him enough.”
Stokes said: “He knows how much value I place on him as a player. I guess it might make him a little tougher every now and then if I ask him to bowl an extra over.”
“The fact that he is where he is now, considering where he was six months ago, is a testament to his character.”
“You can see why we think so highly of him, that he can go through something like that and then come away here with 10 wickets in a test match.”
After Carse's wickets gave England a target of 104, 21-year-old debutant Jacob Bethell smashed his maiden half-century off 37 balls, including the winning runs.
Bethell batted at number three in this match for the first time in his first-class career.
He scored 10 in the first innings but didn't look out of place against quality New Zealand bowling.
Stokes said: “The batting in the second innings was very special.
“He didn't get the runs he would have liked in the first innings, but the way he held himself throughout the batting… If he sticks with that mindset, he'll go far.”
Bethell took the place of regular number three Ollie Pope, who slipped to number six as he kept wicket following an injury to Jordan Cox. Pope made 77 and had a clean game behind the stumps.
Durham's Ollie Robinson is another option for the England squad.
Asked whether Pope would keep the gloves for the rest of the series, Stokes said: “We had a problem and we solved it.”
“That was the composition of the team for this game and we will see it in Wellington.”
