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New Zealand created some great opportunities but was unable to pierce the English defence.
England will now play Olympic champion Argentina in the quarterfinals, while the Black Sticks will be left to reflect on a disappointing campaign which produced one win and one draw in four games.
The Black Sticks started well against England but failed to capitalise on some promising plays.
England absorbed the pressure and pounced with five minutes to go in the second quarter. Phil Roper found himself on the end of a well-placed overhead pass and drove along the baseline.
He laid the ball back for Will Calnan, who deflected the ball into the net.
Then just before the end of the third quarter, England doubled its lead from a penalty corner.
The initial shot rebounded from the post but Luke Taylor swept the rebound past Richard Joyce.
Stephen Jenness and Nick Ross both had good opportunities to pull a goal back for the Black Sticks in the fourth quarter, but England goalkeeper George Pinner stood tall.
New Zealand took off goalkeeper Richard Joyce with 10 minutes remaining to gain an extra field player, but the ploy did not change the scoreboard as the English side held on.