Chasing a modest 221 for victory, Edwards played a captain's knock, scoring an unbeaten 106 off 121 deliveries with the help of 15 fours to take England to 222 in 47 overs.
Apart from Edwards, Lydia Greensway (31), wicket-keeper Sarah Taylor (28) and Arran Brindle (27) also made useful contributions with the bat to guide England home.
Off-spinner Lucy Doolan was the most successful bowler for New Zealand scalping three wickets for 50 runs, while pacer Sian Ruck picked up two wickets for 20 runs.
Earlier sent into bat, Amy Satterthwaite struck a fluent 85 to guide New Zealand to 220 for eight.
Left-arm spinner Holly Colvin shone with the ball for England, picking up three wickets for 31 runs while Aaran Brindle (2/38) dismissed two Kiwi batswomen.
England's chase, however, did not start on a good note as the defending champions lost opener Danielle Wyatt (5) early.
Edwards, who became the first woman cricketer to amass 5,000 runs in ODIs, Taylor then forged a 78-run second-wicket stand, before Taylor was caught off Doolan's bowling.
The English skipper then added 53 runs with Greenway for the third wicket to steady the innings and just when it seemed that the two were set for a long haul a brilliant diving catch by New Zealand captain Suzie Bates cut short Greenway's stay.
All-rounder Brindle then shared a 58-run stand for the fourth wicket with Edwards to take England closer before they lost wickets in quick succession to be reduced to 202 for 6.
But Edwards and Laura Marsh held fort and saw England home without any further trouble.
New Zealand: 220 for 8 in 50 overs (Amy Satterthwaite 85; Holly Colvin 3/31).
England: 222 for 6 in 47 overs (Amy Satterthwaite 106 not out; Lucy Doolan 3/50).