Japan's game plan focused on very structured defensive lines, extremely quick counter-attack and skilful aerial passes to create great opportunities, allowing them to open the scoring through a penalty corner from Shihori Oikawa in the 24th minute.
And the visitors came out firing immediately after the halftime break, awarded two penalty corners in the first two minutes and seeing Hazuki Nagai score from a direct drag flick low to the keeper's right.
Things started to go New Zealand's way when McCann got a nice touch in the 50th minute to get her side on the board and, with two minutes to play, Hayward snatched a share of the spoils from a goalmouth scramble.
In earlier games, two of the tournament's more fancied teams United States and Australia drew 1-1. Argentina beat Korea 2-0 thanks to a couple of penalty corner goals, while China broke down a determined India defence to win 2-1.