New Zealand had a number of chances to equalise on the counter but couldn't convert their opportunities and were down 1-0 at quarter time.
A tight second period seemed destined to finish without a goal until Bates deflected a 40-metre pass from Ashley Fea seconds before halftime.
Officials momentarily discussed whether there was enough time on the clock before agreeing that the goal stood, giving Australia a commanding two-goal lead at the main break.
Spurred on by conceding the last-gasp goal, the visitors burst out of the gates in the second half and should've cut the lead when Rachel McCann found herself in front of goal.
But she was turned away by goalkeeper Jocelyn Bartram, who also denied New Zealand captain Stacey Michelsen and Kelsey Smith to preserve their lead at the final change.
It wasn't until the fourth quarter that the Black Sticks earned their first penalty corner, however they were still unable to find a way through Australia's defence.
The Hockeyroos conceded just one goal in their three matches during the tournament.