Root delighted to join 10,000 club and be a match-winner for Stokes
England started a new era with Stokes as captain and Brendon McCullum as head coach by chasing down a target of 277 at Lord's on day four to take a 1-0 lead in the three-match series.
The prolific Root became only the second England batter to score 10,000 runs in the longest format with a majestic unbeaten 115, combining with the excellent Ben Foakes (32 not out) for an unbeaten stand of 120 under grey skies in London.
Root is the 14th player to reach that milestone and got there at exactly the same age - 31 years and 157 days - as his former team-mate Alastair Cook.
Man of the match Root was untroubled as he made a 26th Test hundred in his first international since stepping down as skipper.
Root was delighted to step up for his former vice-captain Stokes, who made an important half-century on Saturday, and seal England's first win in 10 matches in the longest format.
He said during the post-match presentation: "The number of times Ben has won us Tests under my leadership, it's a great chance for me to give back to him. I love batting.
"I want to score as many runs as I can and win us as many Test matches as I can. As long as I've got the energy and the drive to do it, I'll do it. I couldn't wish for a better person to be leading this team."
He added: "It feels fantastic, more than anything for us to have won this Test match after such a long time. It's been so enjoyable.
"Hopefully we can use this as a way to step forward."
Stokes saluted Root for ensuring his reign got off to a dream start.
"Scoring a hundred and 10,000 runs - what a player, what a man," he said.
Stokes knows England remain a work in progress after they edged in front in the three-match series.
He added: "It was a great Test match. It always seems to be, England v New Zealand - especially at Lord's. Regardless of being captain, the first Test of the summer always has a special buzz about it.
"It was a special week with all the build-up and to come away with the win makes it even better. We're happy leaving here with a win but one thing that everyone needs to take into account is that it's a change of mindset for everyone and it's not something that's going to happen overnight."