Nicholls, 29, survived multiple dropped catches at Wellington's Basin Reserve as he snapped a 21-month string of low scores with his sixth test century.
At stumps, Nicholls was 117 not out with Kyle Jamieson on one. From being on the ropes at three for 78, Nicholls said New Zealand now considered 400 would be "a good result".
New Zealand won the first test inside four days on the back of Williamson's towering 252, but they are now playing without their talismanic captain who is on paternity leave awaiting the birth of his first child.
It was left to Nicholls to prop up the innings, but he had to survive dropped catches and even a technical malfunction, when a broken stump mic prevented a review, to bat New Zealand out of a hole.
"You just try and move on from them same as when you're hitting a boundary or anything else," Nicholls said, describing how he shut his near-misses out of his mind.
"It's just batting, it's cricket, it's pretty fickle so I just keep focusing on what I'm doing and bringing their bowlers back for more spells.
"It was nice in the initial bit to get through to lunch. Just little milestones on this surface."
Everything went the West Indies' way at the start of the day when Jason Holder won the toss and made New Zealand bat on an emerald surface with cloud cover and a howling northerly wind.
After a couple of expensive early overs, Shannon Gabriel and Chemar Holder led an attack that had New Zealand pinned down with three wickets in the first 90 minutes.
The pitch offered pace, bounce and seam movement and when the bowlers found a good length and moved the ball, they were almost unplayable.
But when it seemed the odds were against the Black Caps, an out-of-form Nicholls stepped up.
When he joined Will Young in the middle, the sun emerged, the wind faded and the momentum swung New Zealand's way.
As the total grew, so did the number of spectators with more than 3 500 in the ground by late afternoon with no crowd restrictions in the largely coronavirus-free country.
BROKE MICROPHONE
Nicholls played his way through a short-ball barrage, passing 50 for the first time in 14 innings but riding his luck as chances were spilt and nicks fell in no man's land.
He was dropped once on 21 and twice on 47, while on 29 a top edge for six sailed just out of the reach of Jermaine Blackwood, who had moved several metres in from the boundary.
A shout for Nicholls to be given caught behind on 70 was turned down after an earlier throw at the wickets had broken the stump microphone, leaving no way for the ball tracker to detect if there had been a faint edge.
"He capitalised on his chances," an exasperated West Indies wicketkeeper Joshua Da Silva said.
"It's frustrating when you drop catches, but we can't do anything about it now so we have to move on to the next day."
When Nicholls passed his century, it typified his risky innings as he shaped to turn the ball through midwicket but top-edged it for two on the offside.
Gabriel, in his 50th test, was clearly frustrated when Darren Bravo dropped Nicholls on 47, but he had reason to smile in his next over when he had Young caught at second slip by Jason Holder for 43.
Nicholls had partnerships of 70 with Young, 55 with BJ Watling, and 83 with Daryl Mitchell.
Watling authored his own demise on 30 when he chopped a wide Alzarri Joseph delivery on to his stumps, while Mitchell was trapped in front by Chemar Holder for 42.
Gabriel was the pick of the bowlers, finishing with three for 57 after removing Tom Blundell (14) and Ross Taylor (nine) before lunch before Young became his 150th test dismissal.
Chemar Holder, on debut, dismissed Tom Latham (27) in the first session and ended the day with two for 65.
NEW ZEALAND: Tom Latham (capt), Tom Blundell (wk), Will Young, Ross Taylor, Henry Nicholls, BJ Watling, Daryl Mitchell, Kyle Jamieson, Tim Southee, Neil Wagner, Trent Boult
WEST INDIES: Kraigg Brathwaite, John Campbell, Darren Bravo, Jermaine Blackwood, Shamarh Brooks, Roston Chase, Jason Holder (capt), Joshua Da Silva (wk), Alzarri Joseph, Chemar Holder, Shannon Gabriel