Skipper Charlotte Edwards led the chase with a knock of 33 after English bowlers restricted the Kiwis to a mere 93 for eight in 20 overs at the R Premadasa Stadium here.
Edwards was named player of the match for her batting and astute captaincy.
Chasing a not-so-challenging total, Edwards started in earnest scoring her runs in 37 balls, and with the help of five fours.
After the skipper's dismissal, wicketkeeper Sarah Taylor (22 off 32 balls) and Lydia Greenway's brisk 19-ball 22 completed the task with as many as 16 balls to spare.
Left-arm medium-pacer Sian Ruck returned figures of two for 22 in her four overs for New Zealand.
Sent into bat, the Kiwis could never really challenge their English counterparts from the moment the Greenway-Taylor combo ran out New Zealand skipper Suzie Bates in the very first over of the match.
The Kiwis failed to recover from Bates' early dismissal, losing wickets at regular intervals against some disciplined bowling.
For England, Danielle Wyatt and Holly Colvin finished with two wickets apiece, while there was one each for Anya Shrubsole and Laura Marsh.
"It's our best performance with the ball so far. It turned a lot more here. It was tough, but I'm really pleased we got over the line.
Lydia sets the standard for us in the field and it was a good all-round effort," Edwards said.
Bates said: "We knew we'd come up a few short but I'm proud of the way we tried to defend it. When the pitch was slower we didn't adjust. England are the No. 1 side and we knew we'd have to play well."
New Zealand Women: 93 for eight in 20 overs (Amy Satterthwaite 30; Danielle Wyatt 2/15, Holly Colvin 2/15).
England Women: 94 for three in 17.2 overs (Charlotte Edwards 33, Lydia Greenway 22; Sian Ruck 2/22).