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Left-arm seamer Zaheer Khan dismissed Katich lbw for 102 after changing ends just before lunch, the pair having added another 40 to their overnight century stand for the third wicket.
Michael Clarke was on one was at the interval with Hussey on 64 after the touring side had resumed at 189 for two.
India dictated the morning session through some inspired bowling by Ishant Sharma and Zaheer.
Sharma was unlucky when Rahul Dravid at slip dropped Katich in the day's second over.
Australia, who trail 1-0 in the four-match series, are trying to avoid their first series defeat since the 2005 Ashes tour of England.
Australia are looking to pile up a commanding first-innings score to force a result after debutant off-spinner Jason Krejza took eight wickets to give the visitors a fighting chance for a series-levelling victory.
But the tourists added just 42 runs in 24 overs in the first session.
India made 441 in their first innings with Sachin Tendulkar scoring his 40th test century.
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