Australia won the first Test 2-1 on Thursday, and fought back to secure a 3-3 draw in the second match, but the two-goal defeat on Sunday gave the Kiwis the edge.
The Hockeyroos needed only to tie the final game, but were unable to restrict the Kiwis in the second half, conceding an unanswered two goals.
Skipper Kayla Sharland led the way for the Black Sticks in midfield, and helped the visitors turn the pressure on the hosts throughout the second half, after Claire Messent levelled the scores just ten seconds before the break.
Goals to Clarissa Eshuis and Stacey Michelsen sealed the result for New Zealand, and their third Oceania Cup in a row.
The Hockeyroos have qualified for next year's Olympics, but have no major tournaments beforehand, having failed to make the Champions Trophy.