Morgan made 62 and Stokes signalled his return to form after a five-month layoff with an unbeaten 63 as England surpassed New Zealand's total of 223 with more than 12 overs remaining.
Stokes scored 12 and took 2-43 in the first match of the series, which was his first appearance for England since his arrest on Sept. 25 after a brawl outside a Bristol, Englnd nightclub.
He had a more imposing influence on Wednesday's match, taking 2-42 from eight overs, contributing to a runout and reaching his a half century from 54 balls, his first 50 in ODIs since his 73 against the West Indies in Bristol on the day before his arrest.
Stokes and Jos Buttler (36 not out) then added an unbroken 56 for the fifth wicket to steer England home in the 38th over.
"We wanted to come back strong after the defeat in the first game," Stokes said. "We felt we'd let ourselves down a little bit in the field.
"I think the lads jumped around that and I think we showed new intensity by the way that we fielded. Then to restrict them to 220 on a pretty decent batting wicket, I think the bowlers did a great job."
Two early wickets to Chris Woakes, two in the middle of the innings to spinner Moeen Ali, two brilliant catches by Jason Roy and four run outs helped England take control of the match.
New Zealand, playing without captain Kane Williamson, who has a hamstring strain, lost opener Colin Munro (1) to the third ball of the second over the first bowled by Woakes then Mark Chapman, for 1 on debut, in Woakes' second over, leaving it 9-2.
Ali bowled superbly to finish with 2-33 from 10 overs, Woakes took 2-42 and Stokes 2-42.
Big-hitting Colin de Grandhomme (38) and Santner, who also played a match-winning role in Hamilton, were the last hope for a New Zealand fightback.
Santner, unbeaten on 63, was left stranded when No. 11 Trent Boult was run out to the fourth ball of the last over.
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