Australia resumed the day at 30 for no loss needing 201 more runs to win the match.
David Warner (25) and Chris Rogers put on 64 for the opening wicket. Warner departed but Rogers continued the charge on his way to 116, well supported by an unbeaten 83 by Shane Watson in a 136-run second-wicket partnership to win the match mid-way between lunch and tea on Day 4.
Pacer Mitchell Johnson was again named Man of the Match for his eight wicket match haul.
Australia will have a rest day Monday before flying to Sydney Tuesday for the fifth and final Test.