Chapman's assault saw New Zealand add 100 runs from the ninth to the 16th overs on the way to 5-207 after being sent in at Auckland's Eden park on Thursday.
West Indies struggled at first against New Zealand's three-pronged spin attack and were 6-94 after 13 overs.
But outstanding hitting by Rovman Powell, who made 45 from 16 balls, Romario Shepherd (34 from 16) and Matthew Forde (29no from 13) saw the West Indies reach the last over needing 16 runs with three wickets in hand.
Entrusted with the final over, Kyle Jamieson conceded fours from the first and third balls, the second of which was a no-ball. Powell was out to the fourth ball, caught by Chapman, who took three catches in the innings to complete a player-of-the-match performance.
The tourists needed six from the last two balls but managed only three runs and finished 8-204.
"The West Indies boys, they're so strong they're never really out of the game," Chapman said. "It was amazing that the boys held their nerve at the end."
Chapman went from 12 off 10 balls to 65 off 22 balls. He hit 24 runs, including three sixes, in the 13th over, bowled by Shepherd, then four fours and a six in the 15th over bowled by Jayden Seales.
New Zealand went from 2-83 after 12 overs to 3-140 after 15, and at the end of the 16th over were 3-163.
The West Indies bowlers sent down 11 wides, many of them trying to put the ball out of Chapman's reach. It was reminiscent of the Toronto Blue Jays walking Shohei Otani during the World Series.
Chapman was finally out in the 17th over, caught by Jason Holder off his own bowling after hitting six boundaries and seven sixes.
After Chapman, Daryl Mitchell made an unbeaten 28 from 14 balls and Mitchell Santner 18 not out from eight balls. Tim Robinson made 39 at the top of the order.
Seales' four overs cost 61 runs.
The teams meet in back-to-back matches in Nelson on Sunday and Monday.
