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The world champions were dismissed for 241 but restricted the White Ferns to 211, bowling New Zealand out in the 47th over in the first of five ODIs between the sides.
Amy Satterthwaite fought to an unbeaten 79 from 87 balls to give the White Ferns an outside chance late in the game, but it was ultimately too much to ask, with England cruising to a comfortable win.
England captain Heather Knight led the way for the hosts with 89 runs.
White Ferns captain Sophie Devine, who made 34 from 59 balls, was disappointed not to chase down England's achievable target, but took the positives out of the game.
"It got pretty close there in the end. It just goes to show that the deeper we take the game, the closer it can get. Really proud of the effort there but we know we've got plenty to work on come game two," Devine said.
"We thought 250 was par on this wicket. I thought it was a pretty sedate wicket, I thought there was a good outfield and we were happy to keep them to that, especially with the start that England got. Coming into the sheds at halftime, we certainly knew we were capable of it.
"We spoke about keeping wickets in hand which unfortunately we didn't do, but we can see the damage that our lower order can do given the chance. If we can hit that 30-over mark with a couple more wickets in hand, it's going to be game on.
"I think that's the positive thing that we're going to take out of it.
"There's so many things that if we had done this better with the ball, with the field or with the bat, I think we would've been on the other side of the ledger. So plenty of positives to take out of today."