Opener Aaron Finch retired hurt after being hit on his right index finger by India quick Mohammed Shami as Australia reached tea on 33 without loss and a lead of 76 runs in the second test on Sunday.

Finch, who was unbeaten on 25, was struck by a searing delivery from Shami as his injury brought the tea interval a few minutes earlier than scheduled.

He had survived several nerve-jangling moments against big quick Ishant Sharma, who was also unlucky not to claim Marcus Harris after first slip Chesteshwar Pujara dropped a tough chance low down to his right when the left-hander was on one.

Shortly before tea, Harris, who was seven not out at the break, suffered a nasty blow when he was hit on the helmet attempting to evade a sharp bouncer from paceman Jasprit Bumrah.

The openers continued Australia's momentum after the hosts bowled out India for 283 to gain a first innings lead of 43 despite captain Virat Kohli's masterful 123.

An enthralling morning session belonged to the peerless Kohli, whose brilliant 25th century came to an end on the stroke of lunch when he edged Pat Cummins to a forward-diving Peter Handscomb at second slip.

Whether Handscomb got his fingers under the ball will be a matter of debate for days to come but the onfield official's soft signal was out and the third umpire did not reverse the decision on review.

Kohli had reached his century in style with a flowing off-drive to the boundary then placed his helmet on the ground, pointed to his bat and made a yapping gesture with his gloved hand.

It was his sixth century in Australia, which matches the tally of the great Sachin Tendulkar, and ended a drought against Australia with just 83 runs in his past seven test innings against them.

Kohli showed no lasting ill-effects from an earlier injury scare when he was struck on the forearm by a searing Mitchell Starc bouncer and required treatment.

After Kohli departed, India cut the deficit through wicketkeeper Rishabh Pant's aggressive 36, including a huge straight six off Nathan Lyon. Pant got invaluable support from Umesh Yadav, who made four not out off 31 balls.

Lyon targeted the pitch's expansive rough patches and cleaned up the tail to finish with 5-67.