Man of the match Boult's Test figures of 10-80 included 9-55 on Friday across two innings of the second Test as he revelled in ideal swing conditions at the Basin Reserve.
In what was easily his best day in 19 Tests, Boult revelled in his mastery of a ball which became responsive once the shine came off.
Less within his control was a spectacular diving catch at point to remove wicketkeeper Denesh Ramdin late in the day, drawing gasps from the small crowd and plaudits from his teammates.
"I don't know how that happened. I kind of threw my body up there and it literally went straight into my hands," he said.
"It was something pretty special and something I won't forget. It was brilliant if I can say that."
Captain Brendon McCullum described the catch as a turning point at a time when it looked like the tourists might grind into the fourth day.
"It was a real sign the momentum was with us and luck was going to go our way.
"To me, that was the pivotal moment because it exposed their bowlers and gave us a real shot."
Boult says the fuller natural length of deliveries from him and Tim Southee, who took five wickets, gave them an advantage over the shorter-pitched focus of the West Indies' pacemen.
He had predicted before the Test that the right mix of breeze and overhead conditions could turn the wicket into a seam bowler's paradise.
"Everything did feel pretty good. It was one of those days when things seemed to happen for me."