Tournament will start on June 1 and will be played in different venues in the USA and the Caribbean
Australia collected another two breakthroughs between lunch and tea after paceman Mitchell Johnson reduced the home team to 106-4.
No. 3 Dravid's 51 from 104 balls settled the situation for a short time, but his 49-run partnership with Sourav Ganguly was ended by Shane Watson.
India also lost Mahendra Singh Dhoni, who was bowled by the part-time spin of Michael Clarke, for 9 before the tea break.
Ganguly was the only recognized batsman remaining and was unbeaten on 38 at tea with his team still 220 behind Australia's imposing first-innings of 430.
Dravid was unhappy to be given out lbw by umpire Asad Rauf to an off-cutter that he seemed to feel he had edged before it hit his pad.
It was Watson's third test wicket and gave him figures of 1-28, but left-armer Johnson was the pick with 3-42.
Johnson dismissed veteran batsmen Sachin Tendulkar, Virender Sehwag and V.V.S. Laxman in an excellent spell of 3-19 in 8.5 overs.
Australia struck twice in the first five overs of the morning to stop the momentum India had created in racing to 68 without loss on the second day.
Strike bowler Brett Lee gained the initial breakthrough with the seventh delivery of the day when he came around the wicket and trapped Gautam Gambhir (21) lbw with a ball that angled in and went away.
Sehwag edged an attempted square drive off Johnson six runs later and Matthew Hayden took a comfortable catch at second slip. Sehwag's departure for 45 was a serious blow for the home side, which needed his attacking play, and the situation worsened when Tendulkar and Laxman were dismissed.
Johnson released a slower off-cutter to Tendulkar, who pushed it to Cameron White at short cover. The crowd went silent and Tendulkar, hoping for a bump ball call, stood still until umpire Rudi Koertzen raised his finger.
Tendulkar, who needs another 64 to pass Brian Lara's test run-scoring record, hit three boundaries in his 13, but left with the side in trouble at 94-3.
Johnson added his third victim when he had Laxman caught behind without scoring.
India v Australia first Test scoreboard
Tea scores on the third day of the first Test between India and Australia at the Chinnaswamy stadium here on Saturday:
Australia 1st innings: 430 (S. Katich, 66, R. Ponting 123, M. Hussey 146, Zaheer Khan 5-91, I. Sharma 4-77)
India 1st innings (overnight 68-0):
G. Gambhir lbw b Lee21
V. Sehwag c Hayden b Johnson45
R. Dravid lbw b Watson51
S. Tendulkar c White b Johnson13
V. Laxman c Haddin b Johnson0
S. Ganguly not out38
M. Dhoni b Clarke9
H. Singh not out12
Extras: (b10, lb7, nb4)21
Total (for six wickets)210
Fall of wickets: 1-70 (Gambhir), 2-76 (Tendulkar), 3-94 (Tendulkar), 4-106 (Laxman), 5-155 (Dravid), 6-195 (Dhoni).
Bowling: Lee 16-5-32-1 (nb1), Clark 14-3-43-0, Johnson 13-3-42-3, Watson 12-2-28-1 (nb3), White 7-1-26-0, Clarke 9-2-22-1
Overs: 71
Toss: Australia
Umpires: Rudi Koertzen (RSA) and Asad Rauf (PAK)
Third umpire: Amish Saheba (IND)
Match referee: Chris Broad (ENG)
Tournament will start on June 1 and will be played in different venues in the USA and the Caribbean
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