The hosts could not capitalise on first-half yellow cards for Anna Richards and Mel Bosman and were made to pay when pacy winger Carla Hohepa danced through to help the Black Ferns to a 7-0 half-time lead.
The teams traded penalties early in the second period before Charlotte Barras touched down and Katy McLean converted to get England back on level terms at 10-10, but Kelly Brazier's penalty 15 minutes from time edged New Zealand ahead again and this time England had no answer.
Flanker Maggie Alphonsi was once again a pivotal figure for England throughout, meeting the fearsome Black Ferns head on, but the home team's early nerves were evident.
New Zealand dominated the opening exchanges and were camped in the England half for much of the first quarter but had no points to show for their toils, Brazier and Emma Jensen both missing early penalties.
They looked to have handed the hosts the initiative when 45-year-old fly-half Richards, playing in her fourth World Cup, was yellow-carded in the 22nd minute. She was joined in the sin bin seven minutes later by Bosman.
England could not capitalise on their two-player advantage, however, and found themselves trailing soon after Richards' return.
The prolific Hohepa, whose two tries in the semi-final helped the New Zealanders thrash France 45-7 on Wednesday, burst through an England defence which had not conceded in three of its four World Cup matches to date, and touched down for a fine opening score - her seventh of the tournament.
Brazier added the extras to give the defending champions a deserved 7-0 half-time advantage but England were by no means out of it.
First five-eighths McLean missed two penalties in the first half but converted one three minutes into the second to reduce the arrears, although Brazier responded in kind 13 minutes later to restore the Black Ferns' seven-point cushion.
New Zealand captain Melissa Ruscoe was then sin-binned in the 57th minute, and this time England did make their numerical superiority count.
Barras powered over the line just after the hour mark and McLean coolly added the conversion to draw England level.
The parity lasted only four minutes, however, before another Brazier penalty edged New Zealand into the lead once again and this time there was no way back.
Ruscoe said after the game: "After our game against them last year we had lost the physical battle and we knew we had to come out here today and front them if we were going to win it and our forward pack definitely did that, it's just fantastic."