The tourists were bowled out for 167 in their first innings, 64 behind New Zealand, who reached 0-32 in seven overs before stumps in Christchurch on Wednesday.
While it might have been incongruous to see Hope sporting large reflective glasses under his helmet in gloomy conditions, his 56 stabilised the West Indies' first innings after the loss of two early wickets.
At the other end Tagenarine Chanderpaul laboured diligently over a half-century from 165 balls. A 90-run partnership between the pair helped the tourists towards parity with New Zealand, whose first innings ended at 231.
The West Indies were 6-157 before a late shower forced players from the field. When they returned, the tail had to face the New Zealand pacers in fading light and the last four wickets fell for 10 runs. Jacob Duffy captured all four to finish with 5-34, his first five-wicket bag in Tests.
New Zealand then had to bat again under darkening skies and reached 0-32, with Tom Latham 14 not out and Devon Conway 15.
Matt Henry bowled with pace and accuracy, applying constant pressure around off stump. He dismissed Alick Athenaze (4), then Roston Chase and Justin Greaves for ducks in the same over and finished the day with 3-39.
Zak Foulkes was last man out for New Zealand on Wednesday morning when their innings resumed at 9-231, and lasted three more balls.
He then dismissed John Campbell (1) with his first ball of the match, for his first Test wicket in New Zealand.
"It was awesome. I didn't think it would happen as quick as it did," Foulkes said.
"I haven't played a lot of cricket (at Hagley Park), but it's awesome to be out here and a great place to play cricket."
When Athanaze fell to Henry, the West Indies were 2-10 and precariously placed, but Hope joined Chanderpaul and the pair mounted the stiffest resistance.
They batted through to lunch and on towards tea, before Hope fell for 56 to a short ball from Duffy.
