Shootout specialist Maddie Hinch was mobbed by her team-mates when she forced the Black Sticks Stacey Michelsen out to the right then swatted the ball away for her third shut-out from four.
Georgia Twigg, Alex Danson and Susie Gilbert had netted for England with Sophie Bray shooting just wide.
New Zealand forced the shootout with two minutes to go when Katie Glynn produced a neat inside-out deflection on a cross from the left. That cancelled out Lily Owsley’s 27th minute close-range smuggling home of an Alex Danson cross from the right.
England now play Australia, the side they lost 3-0 to in the pool stages. The Hockeyroos smashed their way into the final with a 7-1 defeat of South Africa.
England midfielder Laura Unsworth said: “We are delighted with the win. Obviously we didn’t want it to go to shuffles, but we knew that if it had to go to that, we’ve got Maddie in goal and we have some very good takers.
“We are delighted with the win. We are looking forward to taking on Australia again. It was a close match and the scoreline didn’t really reflect it. We know we are in with a great shout against them.
“We are just going to give everything we have got and hopefully come away with a gold medal.
“This tournament was all about building our momentum. We have done that through all the matches. We started out with Wales and we have just been building and building and we put in a really good performance today. They are a tough team and we are happy with the win.”
Tomorrow, England may be without defender Giselle Ansley who took a heavy blow to the ankle late in the game.