Tom Blundell has been confirmed to replace Jeet Raval at the top of the New Zealand batting order for the Boxing Day test against Australia.
Trent Boult produced a masterclass, taking six wickets in 15 deliveries.
Latham was not out 25 with Raval on 17 and New Zealand requiring a further 340 to reach their 382-run target.
Indian-origin New Zealand batsman Jeet Raval got a six off the bowler's head. Bowler was not seriously injured.
Neil Wagner claimed seven for 39 as the West Indies crumbled to be all out for 134 in a first innings that lasted a mere 45.4 overs.
New Zealand wrapped up the South African innings five overs after lunch, with the last six wickets falling for only 56 runs.