England took three fine catches and claimed four run-outs to dismiss the hosts for 223 in Tauranga.
In reply, the tourists lost two early wickets but Stokes put on 88 with captain Eoin Morgan, who scored 62.
Jos Buttler made an unbeaten 36 off 20 balls as he and Stokes sealed victory with 12.1 overs to spare.
All-rounder Stokes, playing his second match after five months out of the side following an incident outside a Bristol nightclub, was named man of the match after also taking two wickets and being involved in two run-outs.
New Zealand, who were without injured captain Kane Williamson, looked likely to be bowled out for an even smaller total but Mitchell Santner’s maiden one-day fifty helped them recover from 147-8.
The third game of the five-match series is on Saturday at 01:00 GMT in Wellington.
Improved fielding sets up impressive win
England were criticised for their fielding performance in the opening match in Hamilton but a significantly improved showing went a long way to securing victory.
First, David Willey took a fine catch running back from square leg with the ball dropping over his shoulder to dismiss Mark Chapman, as opening bowler Chris Woakes took a wicket in each of his first two overs.
Willey pulled off a second moment of brilliance to run out Ross Taylor, who scored a century in the Black Caps’ win on Sunday, for 10. Fielding at backward point, Willey dived low to his right to stop Taylor’s cut before spinning and throwing at the stumps while still on the turf.
Opener Martin Guptill offered resistance with a half-century but fell when Jason Roy clung on to a low diving catch at deep mid-wicket.
In the following over Roy took an even better catch at backward point, taking the ball one-handed high to his right as Henry Nicholls became Stokes’ first victim.
Jonny Bairstow ran out Colin de Grandhomme with an accurate throw from the deep before Stokes claimed two run-outs of his own.
The first saw the back of Tim Southee following a fumble at mid-wicket, while the second brought an end to the New Zealand innings with two balls remaining as Trent Boult pushed for a second run.
Stokes and Morgan spearhead England pursuit
New Zealand’s top order struggled, hitting only seven fours in the opening 19 overs. In comparison England found the boundary with ease – 16 times in the same period – but they too lost early wickets.
Jason Roy fell for eight, pulling to Santner at mid-wicket, and Joe Root went for nine as De Grandhomme took another stunning catch low to his right at mid-wicket to leave England 47-2.
Opener Bairstow looked in fine touch before guiding a catch to third man to depart for 37 and leave England 86-3, but any doubts the tourists would win were taken away by Morgan and Stokes.
Morgan hit three sixes and six fours – three in succession in one Boult over – in a fluent innings, although Tom Latham and Nicholls dropped difficult chances to dismiss the captain.
Stokes looked a little shaky early on and was almost run out before taking a nasty blow to the hip after mistiming a pull shot, but improved dramatically as his innings developed.
He showed his typically powerful batting with a number of pulls and a brutal six down the ground off Boult, walking down the wicket to the pace bowler.
It was a surprise when Morgan tamely chipped a return catch to Colin Munro with 49 runs needed, but Stokes continued to bat fluently and Buttler hit Santner for six to secure a comprehensive victory.
‘I was emotional’ – what they said
Man of the match Ben Stokes on Sky Sports: “I was a bit emotional tonight walking off that field being not out.
“It’s an amazing feeling to be back in among the team. It was the one place I wanted to be – back and representing my country.
“It has been frustrating but it’s all about building for the future. Hopefully this is a stepping stone, with all the games we’ve got coming up.”
England captain Eoin Morgan: ”We certainly raised our level of intensity and particularly set the tone early on with the ball, and that was backed up by our efforts in the field. It’s as good a fielding performance as we could have ever hoped for.
“Ben Stokes is a big character, he lifts everybody in the side when he plays like that so it’s great to see him back in fine form.”
Former England bowler Graeme Swann on BBC Test Match Special: ”In motor racing terms, they got ahead at the first corner and lapped New Zealand about 15 times.
“They were smashing the ball out of the park left, right and centre. Ben Stokes was magnificent, Eoin Morgan was exceptional. I would give them 10 and a half out of 10.”
Stand-in New Zealand captain Tim Southee: “We scrapped through to something that we could bowl at. It’s never easy when you hand the opposition four run-outs. We were a little light.”
