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Gayle, who was playing his first Test for more than 18 months due to his stand-off with the West Indies Cricket Board following comments he made about officials in a radio interview, finished on 85 not out.
The 32-year-old hit four successive boundaries off the first over from Chris Martin and added another six in reaching his 34th Test fifty.
Kieran Powell was unbeaten on 58, making his third Test fifty. The 22-year-old's runs came off 164 balls and included 10 fours.
New Zealand were only able to add 119 runs to their overnight tally of 232 for four before being dismissed in the afternoon session.
It would have been even worse for the tourists but for a counter-attacking 39 off 31 by number 10 Doug Bracewell, who put on 42 for the final wicket with Martin.
Spinner Sunil Narine took his maiden five-wicket haul, finishing with five for 132 after adding two more wickets to his three scalps from day one.
The West Indies have dominated the tourists so far this summer, taking the Twenty20 series 2-0, in which Gayle was awarded man of the series, and the ODI series 4-1, in which Gayle made an aggressive century and half-century.
