After absorbing plenty of English pressure the Black Sticks eventually worked their way back in to the game and won a couple of penalty corners late in the first spell but they were unable to convert their chances.
After their early worries the New Zealanders also managed to add some steel to their defence as they kept the English attackers largely in check.
As the game progressed the Black Sticks managed to assert a level of dominance on the contest but struggled to find the elusive last touch.
Wellington striker Stephen Jenness started the game from the bench with a hand injury and he appeared to play through the pain as he had a glove on his hand.
Jenness managed to turn provider with only seven minutes left in the contest as he laid on a ball for veteran Phil Burrows who found the back of the net to draw the sides level.
New Zealand surged in the final few minutes but were unable to find a winner.
New Zealand's quarter-final will be played on Thursday.
England 1 (Mark Gleghorne 11) New Zealand 1 (Phil Burrows 63) HT: 1-0