For long periods it looked like there would be no game at all after persistent if relatively light rain fell throughout the early evening at Hove.
A break in the weather finally allowed play to begin, albeit in damp and muggy conditions.
Danni Wyatt, who hit a match-winning 76 in the first T20 at Southampton on Saturday, fell for a three-ball duck as New Zealand made a good start after winning the toss.
But England responded aggressively, with fellow opener Maia Bouchier hitting a rapid 23, while Capsey’s spritely innings included two fours and two sixes.
The biggest shot of the day though went to Nat Sciver-Brunt, whose huge booming six off Lea Tahuhu went out of the ground.
New Zealand made a poor start to their reply, losing Sophie Devine and Amelia Kerr in the powerplay to slip to 12-2.
They never really recovered, with Dean removing Suzie Bates and Brooke Halliday in the same over to slip to 31-4.
When Jess Kerr edged a Sophie Ecclestone delivery through to Heather Knight the game was all but over as a contest, before more rain swept over the ground to force the players off the field.