After winning the toss and deciding to bat first New Zealand were bowled out in the 34th over for just 156.
Brooke Halliday top scored with 51.
England reached their target in the 22nd over with Tammy Beaumont and Maia Bouchier putting on 137 for the opening wicket.
The Ferns made a decent start with the bat with Suzie Bates making 16 and Georgia Plimmer 29 before she was run out.
However the rest of the batters didn't add much with Amelia Kerr making 10, captain Sophie Devine 13 and Maddy Green 2.
Halliday kept the middle order together for a while with her 51 coming off 60 deliveries, but she quickly ran out of partners.
England spinner Charlie Dean finished with four wickets for 38 runs.
The England batters had few problems against the New Zealand attack with Beaumont's 76 coming off 69 balls and Bouchier's 67 off 50 balls.
Devine tried seven bowlers with Haillday picking up the only wicket.
"Really disappointed," Devine said afterwards.
"We got a really good start with the bat but England came back.
"We need to put this behind and come back harder with important series coming up.
"We've got to identify areas we need to improve but also look at positives, especially Plimmer and Halliday.
"We know we'll have to score 250-260 for which we were on course but lost wickets. On outfields like this we can score naturally."
Game two of the three match ODI series is in Worcester on Sunday night.
