Australia edged closer to sealing a series victory over Sri Lanka as Matthew Kuhnemann and Nathan Lyon took seven wickets each on day three in Galle.

Angelo Mathews (76) and Kusal Mendis (48 not out) had breathed life into the second Test with a 70-run partnership, but Beau Webster's late wicket put the tourists on the brink by the close of Saturday's play.

Alex Carey and Steve Smith's magnificent partnership of 259 ended less than 20 minutes into the day's play, with the latter bowled out by Prabath Jayasuriya (5-151).

Australia's lower order could only add 84 runs to their overnight total, with Webster (31) top scoring for the tourists as they built up a lead of 157 runs.

However, Sri Lanka then slumped to 39-3 by the 14th over of their innings, with Pathum Nissanka (eight), Dimuth Karunaratne (14) and Dinesh Chandimal (12) falling in the opening exchanges.

Chandimal was bowled out by Lyon, who claimed his 550th Test wicket, with the spinner following that up with the important dismissals of Mathews and Kamindu Mendis (14).

Jayasuriya then fell on the final ball of the day, handing Sri Lanka a lead of 54 runs with two wickets remaining, with Australia on course to seal the series on day four.

Data Debrief: Australia's bowlers do the damage

Australia know that only a monumental effort from Sri Lanka can halt their chances of a 2-0 series victory, with their bowlers starring on day three in Galle.

Lyon has now taken 550 Test wickets for Australia, only behind Glenn McGrath (563) and Shane Warne (708) on the all-time list for the Aussies, while he ranks seventh among bowlers to have taken the most wickets in the format.

But the foundations were laid by Carey and Smith's partnership. In another batting record for Australia in this series, it was the highest fourth-wicket partnership by a visiting pair in Sri Lanka in Tests, bettering the 258-run stand between Michael Hussey and Shaun Marsh in Pallekele in 2011.

Carey also overtook his highest first-class score of 143 in style with a firm sweep that rocketed to the boundary, moving past Adam Gilchrist's 144 as the highest score by an Australian wicketkeeper in Asia.