The West Indies require a further 113 runs to make New Zealand bat again after a Test-best performance by Trent Boult (6-40) saw them skittled for 193 on their first innings' reply to the home team's 441.
Shivnarine Chanderpaul was not out 18 at tea with Denesh Ramdin on 15. Tim Southee has so far been the main destroyer with three for 24.
It was the second time in consecutive Tests the Windies have been forced to follow on. They rose to the challenge in the first Test in Dunedin with 507 in their second innings, built on a double century by Darren Bravo.
The West Indies had made a confident start to wiping out the arrears with Kieran Powell (36) and Kirk Edwards (35) putting on 74 for the first wicket, helped in part by the need to rest New Zealand's swing spearheads Boult and Southee.
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They bowled unchanged through 12.5 overs in the morning session to take the final six West Indies wickets and were taken out of the attack in the second innings after two overs apiece.
In a nine-over spell he took three wickets, starting by softening up Powell with a bouncer and following up with a full delivery that swung into the stumps.
Edwards was caught in the gully by Kane Williamson and Marlon Samuels was comfortably caught by Anderson at third slip for 12.
When Boult returned to the attack shortly before tea he claimed Narsingh Deonarine (12) who edged a widish delivery back on to the stumps.