New Zealand, who won the toss, lost three wickets in the first three overs before reaching 30 for three when the players were forced off the Sydney Cricket Ground.
Australia lead the Chappell-Hadlee Series 1-0 going into the final match on Thursday but New Zealand would retain the trophy with victory over the world champions in Hobart.
Brett Lee had Lou Vincent caught by Ricky Ponting at second slip with the second ball of the day and Nathan Bracken forced Jamie How to edge a simple catch to Matthew Hayden in the slips.
Brendon McCullum, who made 96 in the first match on Friday, tamely hit a slower delivery from Lee straight to Brad Hogg at mid-off to leave New Zealand reeling on 12-3.
