Hodge edges towards century as West Indies 310-4, trail by 265
Hodge needs 17 runs after the interval for his second Test century having negotiated some tricky moments throughout the day.
Justin Greaves was not out 20 at the other end.
Hodge, who has faced 170 balls, rode his luck at times, edging short of the slip fielders several times and was dropped on 64 by Daryl Mitchell.
Tevin Imlach and Alick Athanaze fell during the middle session as New Zealand spinner Ajaz Patel did away with his unwanted record of being the bowler to take the most Test wickets without a single one at home.
Patel's 86th Test wicket was his first in New Zealand, bowling Athanaze 2,562 days since his first Test in New Zealand and with his 394th ball on home soil.
England's Billy Bates, who took 50 wickets between 1882 and 1887, all in Australia, has regained the unwanted entry in the Test history books.
New Zealand started the session brightly as Imlach fell for 27 in the second over after lunch without adding to his score, caught behind by Tom Blundell from the bowling of Michael Rae.
Hodge and Athanaze then combined for a 61-run partnership with the latter playing a series of nice drives and flicks as he looked to find form.
Having confidently moved to 45 a moment of indecision saw Athanaze gift Patel his wicket.
He attempted to leave a ball well down the legside, only for it to deflect off his inner thigh and on to the stumps.
The West Indies resumed on Saturday at 110-0 and added only one run before Duffy made the breakthrough in the second over of the day.
John Campbell edged Duffy to Tom Latham at second slip without adding to his overnight 45.
It ended the first West Indies century opening stand since February 2023.
After showing little threat on the evening before, New Zealand's bowlers settled into better lengths in the morning session.
Duffy doubled up when he bowled Brandon King, who had begun the day on 55, for 63.
Wicketkeeper Imlach was promoted to bat at number four after Shai Hope spent the whole of the second day at the team hotel with illness.
Hodge brought up his 50 from 85 balls, guiding Patel backward of point for his ninth boundary an over before lunch.
New Zealand declared their first innings on Friday at a mammoth 575-8, anchored by Devon Conway's epic 227 and captain Latham's 137.