Play had been delayed until 0300 GMT (0830 IST) after heavy overnight rain had caused a sodden outfield.
Daren Ganga was on 23 not out and Brian Lara, who had scored just seven runs in four innings in the series, was battling on 17 after New Zealand captain Stephen Fleming had won the toss and chosen to bowl in cool and overcast conditions.
Lara, who casually flicked the first ball he received from nemesis Shane Bond to fine leg where it dropped just short of Chris Martin, also survived a confident lbw appeal from Nathan Astle just before the break.
Bond had dismissed Lara twice this series, both on the first ball the Trinidadian faced from the fast bowler.
Gayle had provided West Indies with a breezy start, stroking five boundaries in his 27-ball 30, before he was trapped by a brilliant piece of captaincy by Fleming.
The New Zealand captain bought in a short cover after Gayle had scored several runs through the area from aerial shots, only for his next attempt from a short Chris Martin delivery to be easily snapped up by Peter Fulton.
Lara survived his first ball from Bond, who returned to the side after withdrawing from the second Test with a stomach virus, and scratched his way through to the break.
Ganga was also under pressure from New Zealand's bowlers with several tight lbw appeals being turned down.
New Zealand have wrapped up the series after a 27-run victory in the first Test in Auckland and the 10-wicket win in Wellington.