Brooks reached his fourth ODI half-century from 58 balls, and had faced 91 deliveries when he was out for 79 in the 34th over on Wednesday with the the home team reaching their 191-run target with 11 overs to spare.
Earlier, after choosing to bowl, Akeal Hossain took 3-28 and Alzarri Joseph returned 3-36 as West Indies bowled out New Zealand in 45.2 overs at Kensington Oval, Barbados.
It was the first time New Zealand have been dismissed in a 50-over match since March 2020.
"Watching the Kiwis bat I realised it was a bit tough going early for them," Brooks said.
"I guess credit must go to our bowlers for reducing them to a score of 190.
"I was just focused on going out there, getting some partnerships and getting that total off."
Rain breaks punctuated the West Indies innings but couldn't disturb the steady momentum set by Brooks and Pooran, who was out for 28 immediately after the second rain delay.
Hosein, Joseph and debuting spinners Kevin Sinclair (1-37) and Yannic Carriah (1-49) turned the tide of the New Zealand innings with accurate bowling in the middle overs on a pitch which rewarded spinners with bounce.
The Black Caps made a solid start with a 41-run opening partnership between Martin Guptill (24) and Finn Allen (25), but fell to 2-53 when both were dismissed.
Captain Kane Williamson (34 from 50 balls) attempted to lead a New Zealand recovery but lacked support.
The Kiwi tail often comes to their rescue but on this occasion there was no fightback. Mitchell Santner was out for 25 with the total 8-189 and the last two wickets fell quickly.
"Obviously it was challenging out there to get some rhythm and some momentum," Williamson said.
"Credit to the way the West Indies bowled. They got a lot out of that surface and executed their plans well and ultimately played a very good game of cricket."
The second game will be played Friday at the same venue.
