Williamson was unbeaten on 161 when play was finally abandoned at Kensington Oval, with the Black Caps 331-7 as they hunt a rare series win in the Caribbean.
Heavy rain had earlier halted play midway through the session after lunch but, when play resumed nearly three hours later, there was only time for another four overs before the skies opened again.
That still allowed enough time for Tim Southee to fall, chipping an easy return catch to Jerome Taylor three overs after the restart.
New Zealand’s innings was anchored around 23-year-old Williamson, who brought up his seventh Test century before cantering past his previous best of 135.
He shared in half-century partnerships with Jimmy Neesham (51) and BJ Watling (29) as the Black Caps added 191 for the loss of just two wickets after starting the day badly.
The tourists, resuming on 123-3, lost captain Brendon McCullum early, but Williamson and Neesham combined to add 91 for the fifth wicket.
Williamson, who offered two chances early in his innings, took the attack to the West Indies and added 79 with Watling to take their lead to almost 300 before rain intervened.
Kemar Roach, who removed Watling after lunch to pick up his 100th Test scalp, had the best West Indies figures of 4-55.
New Zealand last won a Test series in the West Indies in 2002, when the Stephen Fleming-led Black Caps cruised to a 204-run win in the first Test before drawing the second.