England were in trouble at 101-8 but again, the hosts' tail wagged too much for New Zealand's liking, adding 77 for the final two wickets, two days after a 52-run last wicket partnership proved to be a match-winner in Worcester.
England number eight Katherine Brunt made 49 not out to set up what would be another competitive sub-200 total for the hosts.
New Zealand were in control for much of their innings before late wickets gave England a sniff of victory.
In the chase, Green put on a valuable 72 for the third wicket with Amy Satterthwaite (33) after openers Suzie Bates and Down both fell to Brunt early, leaving New Zealand 13-2.
Green and Satterthwaite kept the required run rate around the 3.5 per over before Satterthwaite was caught in the 24th over, leaving New Zealand 84-3 with work still needed to do.
Sophie Devine arrived at the crease at the ground where she scored 117 three years ago to lead New Zealand to victory but was bowled for four, but a solid 25 from 38 by Brooke Halliday ensured the White Ferns remained in the box seat.
However Halliday, Katey Martin and Hayley Jensen all fell within five overs leaving New Zealand exposed at 158-7. But Green continued her steady innings and Tahuhu smashed two fours and a six in the 46th over to finish off the game with 25 balls to spare.
"Nice to finally get over the line - a little tighter than we'd have liked but we showed some resilience," Devine said after the win.
"We know the tail can do a job and some of that striking from Lea Tahuhu was outstanding. She's been like a caged animal so it's nice to see her bowl like she did. She's turned a corner in terms of accuracy - might not be as quick as she used to be but it's about smarts. We know that we're closing the gap on England and we're trending in the right direction heading towards the World Cup."
The next challenge - to keep the series alive in Derby on Friday and make it back-to-back wins against England for the first time since 2007, and the first time against any team since June 2018.