Wagner took four wickets and two crucial catches at Wellington's Basin Reserve, where the hosts recorded only the second one-run victory in test cricket following West Indies' famous 1993 win in Adelaide.
New Zealand had Wagner to thank for one of the most dramatic outcomes ever seen in the game as he came back from a trouncing by England's batsmen to take the last wicket of James Anderson at the end of a manic day five.
Having set England 258 to win, New Zealand's hopes had faded after lunch as Joe Root (95) and captain Ben Stokes (33) produced a 121-run stand to cut the deficit to 57 runs with five wickets in hand on a sunny Tuesday afternoon.
Enter Wagner, who had bled more than eight runs an over in the third innings when England romped to a 267-run win in the series-opener at Mount Maunganui.
He had both Root and Stokes out slogging in Wellington then nervelessly held catches in the deep to help remove Stuart Broad (11) and wicketkeeper Ben Foakes for 35.
Foakes's wicket left tailenders Jack Leach and Anderson needing seven runs for victory, and Anderson smacked a boundary off Wagner to trim the target to two runs.
Wagner came again and had Anderson caught down the leg side for four to trigger jubilation among his teammates and the home fans in the crowd.
"It's a special one this and we'll celebrate it well," said Wagner, who finished with 4-62 in the fourth innings.
"It's an amazing achievement and obviously everybody contributed, so hats off to everyone. That's what this team's about, just keep playing.
"We keep loving to fight for each other."
With the two-match series ending 1-1, the hosts preserved their unbeaten record at home dating back to 2017.
They also handed England only their second defeat in 12 tests since Stokes and head coach Brendon 'Baz' McCullum unleashed the team's attacking 'Bazball' revolution last year.
Over the home summer, England chased down fourth-innings targets above 250 in three successive tests to whitewash New Zealand. And they will wonder how this one got away from them.
"That game as a whole, in terms of what test cricket's about, was just incredible," said Stokes.
"Wags (Wagner) came on and blew the game open for them. Sometimes things don't happen the way you want them to but it was a good one, wasn't it?"
MOMENT OF MADNESS
England resumed on 48 for one in the morning, then lost four wickets in a hurry to be 80 for five, with Root running out a scoreless Harry Brook in a moment of madness.
But the former skipper shrugged off the mistake and threatened another century after his unbeaten 153 in the first innings.
England pushed past 200 but the momentum shifted again as Stokes threw the bat at a Wagner bouncer and top-edged to square leg where a running Tom Latham took the catch.
An unlikely aggressor through his 113-ball knock, Root also paid for attacking Wagner, sending a miscued pull to Michael Bracewell at midwicket.
Broad tried to slog his team over the line but ramped Matt Henry straight to Wagner at third man to be out for 11.
Foakes and Leach carried England to within seven runs but Foakes pulled captain Tim Southee to fine leg where a scrambling Wagner took a low catch on his knees, leaving the tailenders exposed.
Kane Williamson was named Man of the Match having scored a brilliant 132 in the second innings when the hosts dug deep to put on 483 and defy Stokes for enforcing the follow-on.
England's outstanding rookie Harry Brook was named Man of the Series after 186 in the first innings and twin half-centuries at Mount Maunganui.
The last time a team won after following on was in 2001 when India beat Australia by 171 runs at Eden Gardens.
"It's hard to go past being only the fourth test team to win a test match having been asked to follow on," Southee said.
"The guys just taking it in their stride and giving it a shot in the last three days and managing to come out on top, that's, I'd imagine, would be a test match that will be talked about for a long time.
"(For them) to show that character over the last three days has been very pleasing to see and just an awesome game of cricket to be a part of."
Wicketkeeper Tom Blundell dived to his right to take the Anderson catch, capping a terrific series with scores of 38 and 90 in Wellington and 138 in the first test loss in Mount Maunganui.
"We got a little bit of luck there with a little flick of a bat down the legside," said Southee.
"Tommy Blundell just capped off what has been not just been a great series, but a great 18 months for him as well."
NO REGRETS
Stokes said he had no regrets about enforcing the follow-on.
"Imagine captaining in hindsight?" said Stokes, when asked about the follow-on. "That's nothing that I would ever do.
"It was always our game to lose once we enforced the follow-on.
"But the logic behind it was that our opening bowlers have ripped through their top-order for three innings in a row.
"We knew that New Zealand had to pretty much play the perfect game to put us in a situation like this."
He said England were disappointed with the outcome but being a part of one of the most gripping matches the game has seen was its own consolation.
"Going down to the last day, being in the situation of that last half an hour - it's everything you wish for," he said.
"Even though we came out on the wrong side of it, you can't help but feel blessed that we've managed to be a part of that incredible game.
"It's disappointing to not win, obviously. But we look at the bigger picture of what everyone's enjoyed and seen here today.
"It's probably bigger than the disappointment at the moment."
Stokes's knee remains a concern, and he was in obvious discomfort despite facing 116 balls in his knock of 33 on Tuesday.
He said he had no plans to withdraw from the Indian Premier League to recuperate before the Ashes in the home summer.
"I'm not going to lie. It is very frustrating knowing that I've got something holding me back in terms of my body," he said.
"It's been around for a while ... but we're doing everything we possibly can to allow me to fulfil that fourth-seamer role, like I was able to do two or three years ago.
"Hopefully, come the Ashes, I don't have to worry about it."
