Following on after New Zealand had scored 609-9 declared and having been skittled out on day three for just 213, the West Indies were 168-2 at stumps at the University Oval, still 228 short of making New Zealand bat again.
The West Indies showed some fight in the post-tea session losing just Kirk Edwards wicket to the bowling of Ish Sodhi for 59.
The tourists need to bat the entire day tomorrow and a chunk of Saturday if they are to save the match, reports stuff.com.
Today, the visitors played with more patience and purpose and showed more fight than in the first innings.
The New Zealand bowling unit probed away well, but with less help from the wicket and less help from the West Indian batsmen than in the first innings.
At the close of play, Marlon Samuels was on 17 and Darren Bravo was on 72.
Earlier, New Zealand bowled the West Indies out in their first innings for 213 to record a lead of 396. It was New Zealand's second highest first innings lead, behind the 444 they led by against Zimbabwe in January last year.
Tim Southee took 4-54 for New Zealand, Trent Boult 3-40 and Sodhi grabbed his first two test wickets at home, taking 2-63.
Chanderpaul was the visitor's top scorer with 76 while Bravo scored 40.
