Destined to lose the series after humbling defeats in the first three tests, India also lost three early wickets to start the day with Sachin Tendulkar, Gautam Gambhir and VVS Laxman all departing before lunch on another sweltering morning.
Kohli put on 114 for the sixth wicket with Wriddhiman Saha and the pair almost made it unscathed through the second session before the stand-in wicketkeeper was bowled by Ryan Harris for 35 to bring up the tea break.
The 23-year-old Kohli, under pressure for his place in the side until he hit 129 runs over two innings in Perth, flirted with calamity on 99 before claiming his first century in his eighth test with two runs through the covers.
By then, however, Siddle had removed Ashwin (5) lbw and Zaheer, caught behind for a golden duck, to set up hat-trick delivery which Ishant Sharma defended well.
Sharma lasted 22 balls and had made 16 runs when Hilfenhaus hit his off stump with a fine delivery and the dependable quick returned with a full toss that trapped Kohli leg before.
In Image: Australian players celebrate the dismissal of VVS Laxman