New Zealand opened the scoring in the 21st minute with Anita Punt drilling the ball into the top left-hand corner of the net.
But it did not take long for Argentina to equalise, with Delfina Merino scoring a brilliant half-volley back-hand goal after catching a deflection off Black Sticks goal keeper Sally Rutherford.
The Black Sticks would have still been happy to keep the score at 1-all at halftime, having defended five shots on goal from the hosts.
Argentina had two early scoring opportunities in the second half, which were both well-defended by Rutherford, but they didn't blow a third opportunity, with Merino adding her second goal.
The New Zealand side fought hard to get a goal back over the remainder of the second half, with their best opportunities coming from the late penalty corner attempts, before the clock proved their un-doing.
In the earlier pool B clash, Australia demolished China 5-1. The Kiwi team will meet Australia in their final pool match on Wednesday morning, which is a must-win from New Zealand if they are to avoid the top qualifier from pool A in the quarterfinals.