The phlegmatic right-hander carved out a patient unbeaten 105 which formed the basis of the tourists’ 240 for two, on a flat surface at Sabina Park.
Left-handed opener Tom Latham stroked an enterprising 83 while the prolific Toss Taylor finished the day unbeaten on 34.
Fast bowler Jerome Taylor, in his first Test in nearly five years, was by far the best of the West Indies bowlers with one for 22.
Off-spinner Shane Shillingford was the other wicket-taker but the Windies bowlers toiled with little success on a track offering little assistance to the faster bowlers.
New Zealand, with the good fortune of winning the toss, batted in partnerships after the early loss of Peter Fulton for one.
Williamson added 165 for the second wicket with the left-handed Latham, and then put on a further 66 with Taylor, in an unbroken third wicket stand.
West Indies had reasons for early cheer when Fulton perished inside the first hour, to a catch behind by wicketkeeper Denesh Ramdin, to leave the visitors on nine for one.
Finding a decent line on the top of off-stump almost from the outset, the 29-year-old Taylor got one to bounce and leave Fulton in his fifth over, forcing the right-hander to play and find the edge.
However, Williamson and Latham then frustrated West Indies, to ensure the Black Caps reached lunch at 62 for one, and also saw their side safely through the post-lunch session.
All told, Williamson has occupied the crease for 4-1/2 hours, faced 263 balls and counted 11 fours while Latham, in only his second Test after making his debut in February this year, batted 260 minutes, faced 206 deliveries and hit ten fours.
The pair, however, were forced to survive a testing time in the first session against tall left-arm spinner Sulieman Benn, who extracted bounce and turn to trouble both batsmen.
He thought he had claimed Latham, 25 minutes before lunch to a catch at short leg by Kieran Powell, but the batsman was reprieved on review when replays showed the ball had struck the thigh pad.
West Indies also wasted a review against Latham when the batsman pushed forward to the first ball of off-spinner Marlon Samuels’ spell, but replays revealed an inside edge.
However, the three-man spin attack of Benn, Shillingford and Samuels, failed to find the critical second breakthrough West Indies needed.
There was a huge slice of luck for Latham in the first over after lunch when he sliced a drive off Taylor for Samuels at point to gobble up a smart catch.
However, subsequently replays showed Taylor’s foot marginally over the front crease.
Latham, on 39 at the time, was recalled and proceeded to raise his maiden Test half-century with a single to square leg off Shillingford, 45 minutes after lunch.
He moved to 49 with two boundaries off Benn – the first a lovely drive to cover and the second a streaky shot past point.
Williamson, meanwhile, completed 2000 runs in Tests when he reached 36 and notched his 13th half-century with two boundaries in an over from Roach, 40 minutes before tea.
With the interval approaching, Williamson stepped up the scoring, twice stroking Benn fluently down the ground for boundaries in the bowler’s 21st over.
Unbeaten on 75 at tea, Latham appeared set for three figures before he got a leading edge to Shillingford and gave the bowler a return catch, 24 minutes after the resumption.
If West Indies were sensing an opening, such hopes were quickly dashed as Williamson and Taylor cashed in on some fairly ordinary bowling in the final session.
The right-handed Taylor has faced 66 balls and struck six fours – three of which came in a loose over from Roach in the first over with the second new ball.
Williamson, meanwhile, crept slowly into the 90s but then twice spanked Benn behind point off successive deliveries to reach his century, in the day’s penultimate over.