New Zealand started to fall off tackles and made unforced errors as they wilted, but England were deserved champions.
Earlier in the day, New Zealand had cruised through their quarter-final, blanking Russia 43-0. But they needed a golden point try to Woodman to emerge 12-7 from the semifinal against France after the scores were tied at 7-7 at fulltime.
New Zealand have reduced the competition points' gap on Australia by two. They still sit on second with 64, Australia on 76, and England move up to 60.
This was England's first tournament victory since Houston in 2013.
The fifth and final leg will be played in Montferrand, home of French Top 14 club Clermont, from May 28-29.
England 31 (Heather Fisher 2, Alice Richardson 2, Joanne Watmore tries; Katy McLean 3 con) New Zealand 14 (Sarah Goss, Portia Woodman tries; Selica Winiata 2 con) HT: 19-14