Fulton made one in the first innings in Kingston and has accumulated just 63 runs in his 10 innings since he scored 61 in the first test against West Indies in Dunedin last December.
New Zealand captain Brendon McCullum had decided not to enforce the follow on after Tim Southee wrapped up the hosts' innings for 262, leaving West Indies 246 runs behind the visitors' first innings 508 for seven declared.
Southee and debutant off-spinner Mark Craig had proved to be the chief destroyers in West Indies innings with Southee taking 4-19 from 16.2 overs, nine of which were maidens.
The 27-year-old Craig had been poised to take a five wicket haul on debut before McCullum took the second new ball and Southee wasted little time wrapping up the innings.
Craig, who was impressive with his flight, control and ability to extract bounce and spin from the low, slow-paced, Sabina Park pitch, finished with 4-91 from 24 overs.
"It was nice to contribute to the team and get a couple of wickets," Craig said. "Tim bowled exceptionally well and set the standard ... and it was just nice to chip in for a couple myself."
Craig had sparked a top-order collapse with two wickets in one over, dismissing Kieran Powell (28) and Kirk Edwards in three balls, before leg spinner Sodhi had Darren Bravo caught and bowled for a duck to leave West Indies 61 for three.
Chris Gayle, playing in his 100th test, and Chanderpaul steadied the innings through to 104-3 before Southee had the tall opener caught by wicketkeeper BJ Watling for 64 and then Marlon Samuels trapped lbw for a duck two balls later.
Chanderpaul and Denesh Ramdin produced a partnership of 72 before the captain was tricked by a slower delivery by Southee for 39 in the final over before tea though Chanderpaul (84 not out) marshalled some resistance from the tail as they added 86 runs for the final four wickets.
(Reporting by Greg Stutchbury in Wellington; Editing by Martyn Herman and Ian Ransom)
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