Australia have their backs to the wall in the second Test against Sri Lanka, already trailing by 67 runs with the hosts 6-431 in their first innings at Galle.

Australia insist they can overturn 40 years of history in Sri Lanka and claim a 2-0 series win despite DRS woes leaving them on the back foot in the second Test at Galle.

Sri Lanka went to stumps at 6-431 on day three in reply to Australia's 364, already leading by 67 runs on the first innings.

It came on the back of a fine 118no from Dinesh Chandimal, while Angelo Mathews and debutant Kamindu Mendis joined Dimuth Karunaratne and Kusal Mendis in hitting first-innings half-centuries.

With two days to play, the odds are already firmly stacked against Australia.

Only one team from outside Asia has won a Test when giving up a first-innings lead in Sri Lanka, with losses or draws recorded in all 28 other such instances.

And none have mounted a comeback with the deficit Australia are already facing.

But Australia are adamant they can still win, and are at this stage not willing to settle for a draw and a 1-0 series win.

"We are well and truly in this game," coach Andrew McDonald said.

"Anything south of a 100-run lead or around that gives us a real opportunity. That is probably the reward for batting first.

"This wicket definitely will deteriorate. There have already been some signs of deterioration.

"We think it will still be decent for batting tomorrow and then it might show some signs of deterioration late in day four and then day five."

Sri Lanka's 149-over effort has come after they lost all 20 wickets in just 81.5 overs in the first Test, heavily beaten by Australia in little more than two days.

But this is a far different wicket, so far devoid of the demons that caused prodigious turn in the series opener.

Australia's quicks have also been unable to generate any reverse swing, with the lush wicket square and outfield helping preserve the ball.

The tourists have also only made life harder for themselves after running out of reviews in Sunday's first session.

Chandimal should have been out on 31 when he edged a cut off Mitchell Starc, but Australia had no option to refer the on-field call of not out.

Veteran Mathews was also lucky to survive an lbw shout off Nathan Lyon that would have been out on review, only to fall at bat pad off Starc (2-47) in the next over for 52.

Alex Carey also missed three chances behind the stumps, one an extremely difficult stumping prospect when Chandimal danced down the wicket to Lyon on 10.

Another stumping off Lyon however should have been taken when Kamindu Mendis was on 43, before the debutant was eventually bowled by Mitchell Swepson (2-90) out of the footmarks for 61.

"Sub-continent cricket is always busy around the bat," McDonald said of the missed chances.

"It's difficult in all areas. But one thing is to create a chance, the other is to take it. Unfortunately we didn't quite do it."

The missed chances marked a tough day for Lyon, who finished with Niroshan Dickwella's wicket while battling cramps during his 56 overs for 2-160.

Lyon had started the day by trapping Kusal Mendis lbw in the third over for 85, at which point it looked like Australia could expose the lower order and attain a first-innings lead.

But Chandimal got off the mark by going inside-out and driving Lyon for four and six in consecutive balls, setting the tone for a clinic in playing down the ground.