Ed Cowan top-scored with a gritty 86, while fellow opener David Warner made 71 but India hit back after the visitors reached 109 without loss at lunch.
After a week of negative headlines with James Pattinson, Shane Watson, Usman Khawaja and Mitchell Johnson not considered for selection for disciplinary reasons, Australia's chance to respond was delayed when the first day was washed out.
Brad Haddin replaced the injured Matthew Wade while Nathan Lyon, Smith and Mitchell Starc came in for Glenn Maxwell, Watson and Pattinson, with Clarke moving up the order from five to three.
After winning the toss and electing to bat, It was as comfortable a morning as Australia could possibly have hoped for after chastening defeats in the opening two games of the series.
Warner was the more aggressive - a flat drive down the ground off Ravichandran Ashwin perhaps the highlight - as he reached 50 before lunch, but neither he nor Cowan took undue risks.
Warner did have two small slices of luck, as two edged shots either side of the single which brought up his half-century went to the left and then the right of Virat Kohli at slip.
After lunch, Cowan brought up his sixth international half century in the 40th over, advancing down the pitch to Ravindra Jadeja before clipping the ball through mid-wicket to the boundary.
The pair moved to 137 without loss in the 48th over to register the highest Australian opening partnership in India.
They could only add two more runs before the home side struck. Warner advanced down the wicket to Jadeja and got an inside edge onto his pad before the ball looped up to wicketkeeper Mahendra Singh Dhoni.
With one came two as skipper Clarke - in his only second Test innings at number three - fell to the next ball, stumped by Dhoni off a quicker ball from Jadeja.
The runs dried up as the Australians scored just six from the next seven overs, with Hughes taking 20 deliveries to get off the mark before scoring for the first time in 59 deliveries against spin.
Cowan was given a let-off when his edge from a Pragyan Ojha delivery deflected off Dhoni to Virat Kohli at slip, but he dropped the simple chance.
There was no such let-off for Hughes whose painful innings came to an end in the 60th over when he gloved one behind to Dhoni off Ojha for a 31 ball two to leave the visitors 151 for three.
Steve Smith tried to break the shackles with a mis-timed lofted four off Ojha which trickled to the boundary.
The all rounder found the ropes off Ojha again in the 66th over before hitting the first six of the match off the same bowler.
Cowan was given a reprieve on 85 with Australia on 196 when he was dropped by Cheteshwar Pujara off Ashwin.
However he could add just one more run before his gutsy innings came to an end, as Kohli this time held on to an edge off the same bowler.
Like Smith, new batsman Haddin was keen to make an early impression on the opposition spinners, smashing Ojha back over hit head for a maximum in just the third ball faced.
The pair were noticeably were more positive than those before them, but Smith's approach almost cost him his wicket in the 88th over as he edged a delivery which bounced too low to cut just past slip to the ropes.
The 46-run partnership ended in the 94th over when Haddin got an inside edge on a Sharma delivery to deflect the ball onto the stumps for 21.
Moises Henriques went two balls later after Sharma got one to nip back to leave the visitors 244 for six.
Smith (58no) reached his half century the next over, but he was quickly running out of partners as Peter Siddle was trapped in front by Jadeja for 14-ball duck.
Mitchell Starc smacked 20 off 21, with Saturday vital in the outcome of the match and series.
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