World number two side England saw Lilly Owsley's first-half goal disallowed while Sophie Bray hit the crossbar in the third quarter.
Olivia Merry broke the deadlock in Auckland with five minutes left on the clock when she converted into the top of the net from a penalty corner.
The hosts will now play the Netherlands or South Korea in the final.
England will compete in the bronze medal match on 26 November.
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