A 170-run stand between century-maker Cheteshwar Pujara and captain Virat Kohli put India in a dominant position in the third Test Thursday as Australia's openers survived half a dozen nervy overs before the close.

Dogged Pujara stroked 106 and Kohli 82 before they both fell soon after lunch on what until then had been a lifeless Melbourne pitch.

Rohit Sharma was not out 63 after notching his 10th Test half-century when Kohli called a halt to the innings late in the day at 443 for seven as India go in search of a crucial 2-1 lead in the four-Test series.

That left gave the tourists' attack six overs before stumps to target Australian openers Marcus Harris and Aaron Finch, who battled through to be eight without loss.

Earlier Pujara and Kohli had continued to build their intimidating partnership after coming together when openers Hanuma Vihari and Mayank Agarwal fell on day one.

They batted through to lunch with scarcely an alarming moment as they worked to take the match out of Australia's reach.

But when Kohli started to take on the short ball soon after being seen by the physio for an apparent back complaint in the afternoon session, he was undone by pace spearhead Mitchell Starc.

The Indian run-machine had hit a four and was attempting another boundary next ball when he uppercut to third man for Finch to take an easy catch.

It deprived Kohli of a 26th Test century and the chance to surpass boyhood hero Sachin Tendulkar by making a seventh hundred in Australia. They remain tied on six each.

A stoic Pujara had been unflappable in his 319-ball innings until Pat Cummins sent down a rocket that stayed low, breached his defence and clattered into the stumps.

Pujara, who has scored more runs and faced more balls than any other batsman in the series, added 38 to his overnight 68 in another tremendous knock by a man who has now scored 17 Test tons and two in this series.

It had been an arduous day for Australia's bowlers in hot conditions with Cummins' 3-72 proving the pick.

Sharma, back after missing the second Test with an injury, was in good touch, but had a massive let-off on 15 when he swept a Nathan Lyon delivery to square leg where substitute fielder Peter Siddle made a complete mess of a simple catch, letting the ball pop out of his hands.

Australia's leading spinner finally got a reward in his next over, trapping vice-captain Ajinkya Rahane lbw for 34 as the pitch started to show signs of variable bounce which could spell trouble for the home batsmen.

Lyon had another chance spilled when Cummins fumbled an easy catch from Rishabh Pant near the boundary. Pant finally fell to Starc for 39 and when Ravindra Jadeja went soon after, Kohli made the declaration.

The flat track in Melbourne follows much livelier pitches in Adelaide and Perth which produced results in the four-Test series which is on a knife-edge at 1-1.

Last year's Boxing Day Test saw a dull Ashes draw with England that prompted the match referee to grade the pitch "poor" and there was hope for more juice in it this time round.

Cricket Australia chief executive Kevin Roberts said the pitch would only be fully judged after the Test finishes, but conceded it needed a revamp.

"We need a sense of urgency in the regeneration of this wicket square," he said.