New Zealand were bowled out in the 19th over for 129. Devine again top-scored with 52 - but only two others made double figures.
England's Anya Shrubsole – the woman-of-the-match with six wickets for 46 runs in last year's World Cup 50-over final - took three for 16.
The hosts were relatively untroubled in the chase, reaching 130 for three in the 16th over.
Bates, who became the first White Fern and second woman to play 100 T20 internationals, said their start was too slow.
"Amy Satterthwaite and Sophie Devine's partnership [of 59 from 40 balls for the third wicket] got us back in the game, but we didn't play smart enough cricket with Sophie at the end.
"We were 20 runs short. That made it difficult with the ball, even though the wicket had a bit in it.
"It was disappointing not to bat our full 20 [overs]… that made it difficult for Sophie to kick on."
Bates said the double-header had little impact on their energy levels, given they play 50-over cricket on a regular basis.
"It wasn't about being tired. We got frustrated with the ball and tried too many things."