For more than an hour, England was in trouble but tall midfielder Scott turned things around with a 63rd minute header and a low pass to Jess Clarke for an 81st-minute winner.
England moved into second place in Group B with four points, behind Japan, which beat Mexico 4-0 in the other group game to advance to the quarterfinals. With two 2-1 losses, New Zealand was eliminated.
England now plays Japan in Tuesday's last group game.
''We had most of the play and sheer determination got us the goals and three points,'' said England coach Hope Powell.
Against the run of play, New Zealand scored on a smart counter. Amber Hearn went deep and robbed a defender of the ball and sent a low pass into the center where Sarah Gregorius forced her way in between two defenders to slot home the opener in the 18th minute.
Jill Scott equalized with a most English goal, when the 1.80-meter midfielder rose high in the center to meet Alex Scott's cross from the right and head it forcefully past goalie Jenny Bindon.
To turn things totally around for England, she won the ball in a goalmouth scramble late in the game and calmly set up Clarke for the winner with a shot that went high into the net.
Things long looked bad for England, almost from the start. Its top striker Kelly Smith twisted her left ankle in the eighth minute as she sought to challenge Bindon on a high ball.
She needed long treatment before resuming, but was rarely a factor from then on.
England came off a disappointing 1-1 draw against Mexico while New Zealand lost 2-1 to Japan. It meant both teams needed a victory to maintain a realistic chance of advancing.
Much was expected of England after it beat the United States 2-1 in a friendly ahead of the World Cup. But they have failed to thrill the crowds in two games so far, and in Dresden before a crowd of 19,110, desperation increasingly crept into their game as New Zealand went into a defensive shell and started working the counter.
It took Scott to turn things around.
---
Lineups:
New Zealand: Jenny Bindon; Abby Erceg, Katie Bowen (46, Hayley Moorwood), Anna Green, Ria Percival; Rebecca Smith, Betsy Hassett, Sarah Gregorius (90, Hannah Wilkinson), Katie Hoyle; Ali Riley, Amber Hearn.
England: Karen Bardsley, Rachel Unitt, Faye White (86, Sophie Bradley) , Casey Stoney, Alex Scott, Fara Williams, Jill Scott, Rachel Yankey (65, Jesse Clarke), Kelly Smith, Ellen White, Eniola Aluko (46, Karen Carney).
Referee: Therese Neguel (Cameroon)
