New Zealand had the opportunity to double their lead, missing a penalty corner and also forcing a fine save from England keeper George Pinner in open play.
England began to show signs of frustration. Iain Lewers and Ashley Jackson were both sent to the sin-bin but, after having a goal ruled out following a lengthy review, the home nation salvaged an equaliser when Alastair Brogan reacted quickest in a goalmouth scramble.
Jackson and Andy Hayward both exchanged penalty corners to leave the half-time score at 2-2, but Jackson gave England the lead when - following a controversial call to have the set-piece re-taken because of a New Zealand infringement - he converted another penalty corner early in the second half.
At 3-2, there was a chance for England to put the game out of sight. But they missed a penalty corner and New Zealand responded through Child, who scored his second of the game to set up the shootout.