PERTH - Australia battled through an onslaught from India's fiery fast bowlers on the third day of the second test, building an ominous 175-run lead with six wickets in hand on a menacing Perth Stadium pitch that is expected to deteriorate further.

The hosts reached stumps at 132 for four in their second innings on Sunday with Usman Khawaja 41 not out and captain Tim Paine unbeaten on eight.

Australia, desperate to level the series after narrowly losing the opener in Adelaide, could be without the services of opener Aaron Finch, who retired hurt on the stroke of tea with a possible fractured right index finger.

Under overcast skies, Australia's batsmen faced torrid bowling from India's fired-up quicks with Finch, who was unbeaten on 25, forced off after being hit by a searing delivery from Mohammed Shami.

Marcus Harris, Finch's opening partner, had earlier been hit on the helmet attempting to evade a sharp bouncer from paceman Jasprit Bumrah, who bowled superbly in favourable conditions.

A bewildered Harris fell after the tea break clean bowled by Bumrah for 20 after not offering a shot, and locally-bred Shaun Marsh was caught behind for five while rashly attempting a pull shot off Shami.

Australia's inexperienced batting-order struggled under pressure with Peter Handscomb making an unconvincing 13 before being trapped leg before after shuffling across his stumps to Ishant Sharma, who bowled without luck initially.

Travis Head was dismissed before the close for 19 after needlessly guiding a wide Shami delivery to deep third man, in a mirror-image of his first innings dismissal.

Khawaja, Australia's most accomplished batsman, survived several nerve-jangling moments to compile his highest score in the series.

Australia's impulsive batting almost squandered their advantage after bowling out India for 283 to gain a handy first innings lead of 43 runs, despite a brilliant century from India captain Virat Kohli.

An enthralling morning session belonged to the peerless Kohli, whose 123 came to an end at the stroke of lunch when he edged Pat Cummins to a forward-diving 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 25th century in style with a flowing off-drive to the boundary and 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.

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