Earlier in the day, New Zealand got off to a shaky start losing three quick wickets courtesy a brilliant spell by Cottrell with the new ball.
Taylor (47*) kept going though adding another 32 with Henry Nicholls before an extended rain break put an end to the Black Caps innings on 131 for 4 in 23 overs.
Two wickets to Matt Henry and three to Trent Boult reduced the West Indies to an unthinkable 5-9 inside four overs.
Gayle was in action again the following over with the score still on 26 he caught Colin Munro (21) who flashed at another shortish one outside off this time from West Indies skipper Jason Holder.
Skipper Jason Holder and Rovman Powell put on 48 for the sixth wicket, before the guile of Mitchell Santner (3-15) tempted Powell into an ill-advised slog which was well taken by Lockie Ferguson at third man.
However, after Ross Taylor and stand-in captain Tom Latham got their innings back on track, the rain came and play was suspended for nearly five hours.
"Obviously it was an outstanding performance today", Latham said. After the rain break, New Zealand continued playing before the partnership was finally broken by Windies' left-arm spinner Nikita Miller, who accounted for the unsafe Latham.
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"I think it was about building a partnership with Ross, trying to take it as deep as possible", he said.
"It was nice that. we managed to scrap to a total and the way the boys came out and did the job with the ball was outstanding".
Taylor went on to make 47 off 54 balls, which included six boundaries, while Henry Nicholls smashed a quickfire 18 as New Zealand finished on 131/4. "I don't think we forecast as much rain as there was but it was nice we managed to get back out there, increase the run rate a bit then do the job with the ball".
That duo were at the crease when rain hit with New Zealand 83-3 after 19 overs, with the weather causing a long delay. Henry Nicholls added 18 not out from nine balls as New Zealand posted a competitive total in hard circumstances.
"It's unfortunate with the batting, we lost wickets up front again and were not able to build momentum", Holder said.
Latham survived a review aganinst a leg before appeal off his first ball, but steadied the New Zealand ship with Ross Taylor with a fifty-run stand during which a slight drizzle ensued. The hosts also swept the test series between the teams 2-0.