The West Indies lost 16 wickets on the third day as they handed New Zealand a comprehensive victory by an innings and 73 runs.
It was the Black Caps first win in 11 Tests under Brendon McCullum who replaced Ross Taylor after their last success in Sri Lanka nearly 13 months ago.
"Everyone's obviously very happy," McCullum said.
"We played near the perfect Test match and that's obviously pleasing."
The West Indies resumed Friday at 158-4 in their first innings in reply to New Zealand's 441.
They were forced to follow on when they collapsed to be all out for 193, and the second innings ended at 175.
Boult was the chief destroyer with six for 40 in the first innings where his last four wickets came in the space of six deliveries.
In the second innings he returned 4-40 and also pulled off a spectacular one-handed, diving catch when Denesh Ramdin (19) slashed at a Neil Wagner delivery.
"That catch was pretty surreal, I don't know how to explain that one, I just seemed to dive at it and it stuck," said Boult.
"It's something I'm going to cherish for long time. Ten wickets in a Test match is obviously something very special to me."
The West Indies had success at the start of the match when they won the toss and put New Zealand into bat on a green wicket, but from there they were outplayed.
Tino Best and Shannon Gabriel pitched the ball up in their early overs and had New Zealand at two for 24. But once they dropped off a good length the game slipped away from them.
"We have one Test to save the series but it's going to take a hell of an effort to do that," captain Darren Sammy said, blaming the West Indies fielding for their downfall.
"It's very disappointing ... credit must go to the New Zealand bowlers, especially Trent and the way he exploited the conditions which is something we as a bowling group have not been able to do."
Taylor scored 129 for New Zealand and the tail added significant cameos, including an unbeaten 38 by Boult, as for the second consecutive Test they forged a sizeable first innings following their 609-9 declared in Dunedin.
But unlike the first Test, which fizzled to a draw after the West Indies posted a match-saving 507 when forced to follow on, this time New Zealand did not ease up the pressure.
When the West Indies resumed on Friday Marlon Samuels and Narsingh Deonarine negotiated the first seven overs with relative ease, adding 17 runs.
But, with the first delivery of his fourth over, Boult found the outside edge of Deonarine's bat, Taylor took the catch at first slip and the collapse was underway.
Samuels, who had been the mainstay of the innings, had reached 60 when he found himself rooted to the spot against a swinging Boult delivery and edged the ball to wicketkeeper BJ Watling.
Sammy was bowled on the second ball he faced and Shane Shillingford followed immediately. Best survived the hat-trick ball but was bowled by another swinging Boult delivery on the second ball he faced.
After being forced to follow on, the West Indies made a solid start to their second innings, reaching 75 for one before falling apart.
Apart from openers Kieran Powell (36) and Edwards (35) the only other innings of note was an unbeaten 31 from veteran Shivnarine Chanderpaul.