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.
The West Indies resumed Friday at 158-4 in the 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 figures of 4-40 and also pulled off a spectacular one-handed, diving catch when Denesh Ramdin (19) slashed at a Neil Wagner delivery.
Boult described the outcome as “a great day for me personally and obviously a great day for the team as well”.
“That catch was pretty surreal, I don’t know how to explain that one, I just seemed to dive at it and it stuck.
“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.
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 into 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 with no hint of the destruction that lay ahead.
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.
Darren 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.
Darren Bravo, who rescued the first Test in Dunedin with a double century, was out for a duck.
Apart from openers Kieran Powell (36) and Edwards (35) the only other innings of note was an unbeaten 31 from veteran Shivnarine Chanderpaul.