Boult took four wickets, including all of the top three, as the Windies could establish a second-innings lead of only 121 in the third and final Test which they need to win to draw the series.
New Zealand ended the day, as they had begun it, batting - Ross Taylor's 131 boosted their first-innings total to 349 in the face of six wickets from Sunil Narine, while Peter Fulton and Hamish Rutherford closed out two overs at the end of the day to finish six without loss at the end of the evening carnage.
The writing was on the wall for the Windies in the fifth over when Boult clean bowled Kraigg Brathwaite, then had Kieran Powell caught at slip.
Soon after Boult had Kirk Edwards strangled down the leg side, before Shivnarine Chanderpaul launched the briefest of counter-attacks with a clutch of boundaries.
When Marlon Samuels nicked Corey Anderson behind and Neil Wagner accounted for Chanderpaul courtesy of a fine low catch from Kane Williamson at slip to leave them 46 for five, it was only a matter of time.
Boult came back to trap Denesh Ramdin lbw, before Tim Southee wrapped up the innings with three wickets in an over - including his 100th in Tests.
Narine was the last man standing, and it was he who had put his side in the strong position they so dismally threw away in the evening session by taking six for 91 off 42.3 overs - his best return in Tests - in New Zealand's first innings.
He continued his form from the night before by taking the first wicket of the morning, and his third of the innings, in the eighth over.
Darren Sammy was the catcher again, as he was twice on the previous night, holding on high up at slip as Brendon McCullum slashed at the spinner.
Anderson than combined with Taylor for a partnership of exactly 50, highlighted by the former taking 13 off one Narine over including back-to-back boundaries via a pull and a cut.
But he fell in the next over going for another boundary as he was caught at deep square leg off Veerasammy Permaul, leaving his side 249 for five at lunch.
Sammy took the new ball immediately after lunch and Taylor took advantage with a three and two fours off Tino Best's first over of the session, the last of which - a cover drive - brought up his 11th Test ton and his third of the series.
The new ball did for BJ Watling though as he was caught behind off Sammy in the next over.
Taylor continued to attack, plundering 20 off one Sammy over which included two big leg-side sixes, but his aggression cost him when he cut Best straight into the hands of third man.
Southee and Wagner both added some quick runs but Narine wrapped up the final three wickets, including a classic off-spinner's dismissal which saw Ish Sodhi bowled between bat and pad.