He then took three catches, one being an impressive diving effort in the field to cap off a man-of-the-match performance.
New Zealand made a reasonable start with Tim Robinson and Devon Conway making 45 off the opening five overs. The decision to bowl West Indies opener Matthew Forde out worked in his fourth and final over as he broke the opening partnership by bowling out Conway (16 off 24) in another innings where he failed to fire.
Robinson, 39 off 25, went the following over also bowled, falling to Romario Shepherd which left two new batters at the crease and New Zealand on 59-2.
With Chapman and Rachin Ravindra at the crease and the score sitting at 81-2 at 6.75 an over, they continued to chug the innings before Chapman put the foot down.
First he took 24 runs off one Romario Shepherd over, only for Ravindra to go first ball on the next over, topping Roston Chase high in the air to be caught behind for 11 off 15.
But that didn’t deter Chapman who then hit 23 off a Jayden Seales over with five balls sent to the boundary.
In March, Chapman hit 94 from 44 balls at Eden Park against Pakistan and he looked to top that, reaching his 50 in just 19 balls.
New Zealand’s Mark Chapman celebrates reaching 50 in game two of the T20 cricket series between the Black Caps and the West Indies at Eden Park. Photo / Photosport
Chapman was 12 off 10 then hit 53 off his next 14 balls. But thoughts of a second T20 ton ended when he was eventually caught and bowled by Jason Holder after sending a bouncer straight up.
Daryl Mitchell (28 from 14) and Mitchell Santner (18 from 8) ensured they got New Zealand past the 200 mark.
Jayden Seales, who made 3-32, had a night to forget going for 0-61 off four overs.
Jacob Duffy struck third ball of the West Indies innings, with Brandon King edging behind for a duck after making just three yesterday.
Ish Sodhi, in the team for Jimmy Neesham, then got a wicket with his second ball caught Duffy in the deep to dismiss Alick Athanaze for 33 who mistimed a reverse sweep. That left West Indies 49-2 in a similar start to New Zealand.
They then lost four wickets in four overs which derailed the chase.
Chapman took a diving catch, giving Sodhi his second which removed Ackeem Auguste (7 off 7). Santner began his spell in the 10th over and removed dangerman Shai Hope for 24 when he bowled him.
Jason Holder hit successive sixes off Sodhi but the Kiwi spinner had the last laugh, bowling him two balls with a later with a googly for 16. Roston Chase then departed the next over giving Santner his second and put the visitors in a big hole at 93-6.
Rovman Powell and Romario Shepherd gave them a real chance to dig out including five sixes in six balls as they put on 62 from 24 balls before Shepherd found Michael Bracewell at deep mid-off. But the West Indies kept swinging for the fences.
Only three teams have chased down a score of 200-plus at Eden Park and West Indies looked a real chance after 22 came off a Jamieson over with 30 needed from the last two overs.
Needing 16 off the final over, Jamieson bowled a no ball four which left six off three and swung the match in favour of the visitors. But Powell skied a shot to Chapman for 45 before they could only manage singles off the final two balls.
Another late chase at Eden Park falling just short.
New Zealand 207/5 (Chapman 78, Robinson 39; Chase 2/33)
West Indies 204/8 (Powell 45, Shepherd 34; Santner 3-31 Sodhi 3-39)
Series tied 1-1