Australia's batsmen battled a deteriorating pitch in their bid to build a match-winning lead on the third day of the second Test in Perth on Sunday.

The hosts led by 43 after both teams' first innings despite a superb Virat Kohli century, but found batting incredibly tough in their second innings.

At stumps, Australia were 132 for four, with Usman Khawaja on 41 and Tim Paine on eight, an overall lead of 175.

Although they still had six wickets in hand, opener Aaron Finch was taken to hospital for scans after retiring hurt with an injured right hand on 25.

The cracks in the pitch were starting to become a significant factor, with Finch's opening partner, Marcus Harris, also struck flush on the helmet by a rising delivery in making 20.

The Australians played and missed time and again as they battled to extend their lead, with Jasprit Bumrah (1-25) almost unplayable at times and well supported by India's three other pacemen as they maintained unrelenting pressure on the batsmen.

Shaun Marsh (5) and Peter Handscomb (13) again fell cheaply, doing little to ease the pressure on their pair to retain their spots in the side.

Marsh played a poor shot to a short ball from Mohammed Shami (2-23) and was caught behind, while Handscomb's shaky defence was highlighted when he was trapped lbw by Ishant Sharma (1-33).

Easy as 123 for Kohli

The struggles of the Australian batsmen were a far cry from the command of Kohli as he anchored his team's first innings.

In reply to Australia's 326 after winning the toss and batting, India were bowled out for 283 despite Kohli's 123.

Kohli reached his century with a classic straight drive off paceman Mitchell Starc, having been at the crease for 310 minutes and faced 214 balls.

Two overs later he produced the shot of the match when he lifted Josh Hazlewood over third man for six.

In reaching triple figures, Kohli became the second-fastest player to reach 25 Test centuries in terms of innings with 127, behind only Don Bradman (68) and ahead of his countryman Tendulkar (130).

He also joined Tendulkar as the only Indian batsmen to have scored six Test centuries in Australia, and became the first Test centurion at the new venue.

The Indian captain's innings came to a controversial end when he was caught at second slip by a diving Handscomb from the bowling of Pat Cummins.

Kohli was given out by the on-field umpires but believed it had not carried.

However the decision stood after it was reviewed by third umpire Nigel Llong.

The Indians lost their last five wickets for just 35 runs to hand Australia a small but valuable lead.

Spinner Nathan Lyon was the best of the Australian bowlers, taking 5-67, while Mitchell Starc and Josh Hazlewood both grabbed two wickets each.

India's day got off to a disappointing start with Ajinkya Rahane fell in the first over of the day to Lyon for 51, ending a 91-run stand with Kohli.