At the end of the rain-abbreviated second day, in which only 63.1 of the scheduled 90 overs were bowled, the West Indies trailed New Zealand's first innings of 441 by 283.
Only Kirk Edwards and Marlon Samuels provided any stern resistance with well compiled half centuries. Samuels was not out 50 and Narsingh Deonarine was on 11.
New Zealand all-rounder Corey Anderson, in only his fourth Test, made the crucial breakthroughs for his team, removing first Test double centurion Darren Bravo for four and Edwards for 55.
Southee was eventually rewarded with an lbw decision against Powell on 21 while Boult came back in his second spell to remove Chanderpaul.
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Bravo, unable to reproduce his marathon innings of the first Test, faced 12 balls before he edged Anderson to second slip Peter Fulton.
Edwards, who had looked assured on his way to a half century, was undone by a full Anderson delivery which he tried to turn to the leg side but sent a leading edge to Hamish Rutherford at cover.