The visitors put up 285 for five at stumps, with Marcus North unbeaten on 43 and Tim Paine on eight.
Only 85.5 overs could be bowled during the day as play was called off early due to bad light.
The in-form Shane Watson [ Images ] was the another significant contributor in the Australian innings with a well-made 57.
The Australian innings witnessed three good partnerships but none that could last long to take the game away from India.
The Indian bowlers, on the other hand, took wickets at regular intervals to ensure their side remained in contention.
Morning session: (95 runs, 27 overs, no wicket)
An in-form Shane Watson (57) started on a positive note, with successive boundaries off Sreesanth [ Images ] in the bowler's first over and then another in his third.
Zaheer's sixth over (in his first spell) proved costly for India, 14 runs coming off it, with Watson helped himslef to three boundaries.
Sreesanth, who was taken off after three expensive overs, replaced Zaheer, but Watson was in an unforgiving mood, pulling him through midwicket for what was his eighth boundary.
Harbhajan was introduced into the attack in the 14th over and Simon Katich [ Images ] (43) welcomed him by hitting his first delivery to the cover point fence. The left-hander, after a sedate start, was slowly starting to find his feet.
Meanwhile, a sweep off Ojha to the midwicket, his ninth boundary, helped Watson reach a deserving half century.
It was his 11th Test fifty, his third against India, and his fifth significant contribution (in five innings), the tour match inclusive, in this series.
The Australian opening duo of Shane Watson (54 not out) and Simon Katich (39 not out) frustrated India with some calculated shot-making and some risk-free cricket.
After 27 overs (at lunch), the visitors had made 95 for no loss. It was Australia's best opening partnership at the venue.
Post-lunch session: (93 runs, 30 overs, 3 wickets)
Harbhajan Singh [ Images ] provided India the much-needed breakthrough in the first over after lunch.
Katich started with a boundary off the third ball. However, Harbhajan struck two balls later, having the batsman caught by Rahul Dravid [ Images ] at first slip.
Katich's 95-ball knock was inclusive of seven hits to the fence.
In came Ponting and he opened his account with a boundary through cover point off Harbhajan. However, Ojha struck after a few overs, having Watson caught behind.
Watson's 88-ball knock was inclusive of nine hits to the fence.
Michael Clarke [ Images ] (14) didn't last either, Harbhajan having him caught by Raina at backward short-leg.
And from 99 without loss at one stage, Australia had slumped to 132 for three.
Ponting and Hussey tried to rebuild the innings, combining caution with agrression to good effect. The Australian captain's was an aggressive knock, with a plethora of sweetly-timed boundaries.
Hussey, on the other hand, started on a tentative note - the first ball he faced off Harbhajan dropped just short of Pujara at sllly point - and lived dangerously throughout.
He brought up the 50-run partnership for the fourth wicket with a boundary off Sehwag, the ball almost carrying to the fielder.
Post-tea session: (97 runs, 28.5 overs, 2 wickets)
Zaheer Khan [ Images ] struck soon after tea to bring India back into the match.
The left-arm quick, known for his ability to make good use of the reverse swing, had Michael Hussey [ Images ] (34) caught by Virender Sehwag [ Images ] at gully. Hussey and Ponting had put on a 66-run stand for the fourth wicket and were looking dangerous.
However, Hussey, whose 45-ball knock was inclusive of four hits to the fence, again missed out on a good start.
Ponting though reached his 54th Test fifty, his eighth against India, with a risky shot off Harbhajan that went wide of Dravid and to the fence.
The Australian captain celebrated the same with another boundary, on this occasion a perfect pull shot that went to the midwicket fence.
Marcus North hit a well-timed off-drive off Harbhajan to raech the 1, 000-run mark in Tests.
Ponting, meanwhile, continued with some fluent batting. The duo put on 58 runs for the fifth wicket before Raina struck.
His 147-ball knock was inclusive of a dozen hits to the fence.
North and Paine ensured their was no further damage.
Earlier, Australia won the toss and elected to bat first.
There was three changes to the Indian squad that won at Mohali, an injured VVS Laxman [ Images ] being replaced by Cheteshwar Pujara [ Images ], who made his Test debut; Murali Vijay [ Images ] replaced Gautam Gambhir [ Images ] and S Sreesanth came in for Ishant Sharma [ Images ].
Rookie Peter George replaced an injured Doug Bollinger in the Australian line-up.
Team India's recent record at the Chinnaswamy Stadium is forgettable, to say the least.
The home side has not won a Test at the venue since beating New Zealand [ Images ] in October 1995. And in the seven Tests since, they have lost four and drawn the rest.
Moreover, Australia has beaten the hosts on two of the three occasions in the last 15 years. In fact, India is yet to get the better of Australia at this venue.
India: MS Dhoni [ Images ] (captain), Virender Sehwag, Murali Vijay, Rahul Dravid, Sachin Tendulkar [ Images ], Cheteshwar Pujara, Suresh Raina, Harbhajan Singh, Zaheer Khan, Pragyan Ojha [ Images ], S Sreesanth
Australia: Ricky Ponting (captain), Shane Watson, Simon Katich, Michael Clarke, Michael Hussey, Marcus North, Tim Paine, Mitchell Johnson [ Images ], Nathan Hauritz [ Images ], Ben Hilfenhaus [ Images ], Peter George