From five games at the tournament the Kiwis finished with two wins, two losses and a draw with the result sealing a third place finish.
Head coach Colin Batch said it was pleasing to finish strongly with their best performance at the tournament.
"It was a very good effort from us today, we controlled the game well and scored some impressive field goals," he said.
"We went into the game looking to finish well at the tournament and we certainly did that, it's significant that we played our best match at the end."
"It was a big step up for us and we walk away with the bronze medal which is a good reward for a good performance against one of the top teams who will be at Rio."
A brilliant solo effort from Neal opened the Black Sticks' account.
Neal pivoted and changed angle twice before firing into goal from long range.
New Zealand doubled the lead in the 28th minute after a length-of-the-field counter attack saw Neal pass to Wilson on the post to knock past the goalkeeper.
Captain Child scored his side's third goal of the match early in the third quarter with a deft touch on a hard cross across the circle.
The Kiwis grabbed their fourth in emphatic fashion in the 57th minute with Jenness picking up a loose ball and smashing home on his forehand.
Argentina scored a consolation goal just before fulltime with Gonzalo Peillat converting a penalty corner.
The Black Sticks now travel home to New Zealand for their final preparations ahead of the Rio Olympic Games next month.
Black Sticks 4 (Shay Neal, Nick Wilson, Simon Child, Stephen Jenness) Argentina 1 (Gonzalo Peillat). HT: Black Sticks 2-0.
