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The tourists -- who have not lost a Test series since England won the 2005 Ashes -- were 111-3 at lunch chasing an unlikely 382 to win, with fast bowler Ishant Sharma doing the damage with two wickets.
Matthew Hayden was unbeaten on 46 and Michael Hussey on 14 not out at the break.
India lead 1-0 following their 320-run victory in the second Test in Mohali. The matches in Bangalore and New Delhi were drawn.
Only three teams -- the West Indies (v Australia in Antigua in 2003), India (v the West Indies in Port-of-Spain in 1976) and Australia (v England in Leeds in 1948) -- have chased more than 382 in the fourth innings to win a Test.
Australia went for quick runs in a bid to square the series, but lost overnight batsman Simon Katich (16), skipper Ricky Ponting (eight) and an unwell Michael Clarke (22) in the process.
Katich top-edged a Sharma delivery while swinging across the line, with wicket-keeper Mahendra Singh Dhoni taking the catch.
Ponting failed to beat an Amit Mishra direct-hit from mid-off while going for a risky single.
Clarke, batting with a runner (Katich), was lucky to survive a confident leg-before appeal off Sharma early in his innings as the TV replays suggested the ball would have hit the leg-stump.
He did not last long, edging Sharma to the wicket-keeper.
Hayden offered a difficult chance on 35 when he attempted to reverse-sweep spinner Harbhajan Singh, but slip fielder Rahul Dravid failed to latch on to the ball. He has so far hit four boundaries in his 67-ball knock.
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