Edwards, who officially took charge of the team in 2006, made just five from nine balls on her landmark appearance, but England were able to chase down a modest target of 98 at the Bert Sutcliffe Oval.
The 35-year-old was bowled by Lea Tahuhu, who also accounted for fellow opener Heather Knight (26) and Sarah Taylor (20) which left the tourists on 55-3.
Natalie Sciver (16) and Lydia Greenway (25) put on a decisive stand of 38 for the fourth wicket and although both were dismissed, Katherine Brunt hit a six to get England over the line with eight balls to spare.
Earlier, Edwards had won the toss and her decision to field first was vindicated as the hosts limped to 97-9, with Knight (2-14), Danielle Hazell (2-15), Laura Marsh (2-24) and Jenny Gunn (2-28) each taking two wickets.
Sophie Devine struck a counter-attacking 37 from 31 balls for New Zealand, which included two fours and a six, but her team-mates could not match her efforts.