Lunch Sri Lanka 257 & 98 for 4 (Mathews 38*, de Silva 8* Kuhnemann 2-22, Lyon 2-27) trail Australia 414 (Carey 156, Smith 131, Jayasuriya 5-151) by 59 runs
Retiring Dimuth Karunaratne was unable to provide one final rearguard for Sri Lanka as Australia moved closer to a crushing series victory on a fast-moving day three.
On a very dry, deteriorating Galle surface, Sri Lanka reached tea at 98 for 4 in their second innings with their slim hopes resting on skipper Dhananjaya de Silva and Angelo Mathews, who has shown grit to remain 38 not out.
Given Sri Lanka's batting frailties this series, Australia will be confident of wrapping up the second Test later today.
Trailing by 157 runs on the first innings, Sri Lanka slumped to 39 for 3 when Nathan Lyon claimed his 550th Test wicket after dismissing Dinesh Chandimal for 12. Karunaratne had earlier fallen for 14, caught behind off left-arm spinner Matthew Kuhnemann, bringing down the curtain on his 100-Test career.
Mathews and Kamindu Mendis provided some resistance with a 42-run partnership, but they never looked settled and both received reprieves after missed chances by Alex Carey with the gloves.
Having entered the series averaging over 70, Mendis' tame series ended when he chipped Lyon to mid-off and it appears only a matter of time before Australia clinch their first series victory in Sri Lanka since 2011.
It was a disappointment for Sri Lanka after their earlier fightback, claiming seven wickets in the morning session to bowl out Australia for 414. Left-arm spinner Prabath Jayasuriya found venomous bite with the second new ball to pick up four of his five wickets in the session.
Carey and Steven Smith's magnificent partnership of 259 ended less than 20 minutes into the day's play. 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-stand between Michael Hussey and Shaun Marsh in Pallekele in 2011.
Even though they were buoyed by their efforts with the ball, Sri Lanka faced a tough task in their second innings against an Australia attack that have been all over them in the series.
Opener Pathum Nissanka started well against Mitchell Starc's 145kph bowling with a couple of glorious drives to the boundaries in the opening over.
But Nissanka succumbed quickly to Kuhnemann with indecisive footwork proving costly, bowled by a good length delivery that slid on. Karunaratne tried to muster a final rally and got through tormentor Starc, who had dismissed him nine times previously.
Karunaratne countered Kuhnemann with a lovely flick of the wrists to hit his first boundary of the innings through midwicket. He combined well with Chandimal, Sri Lanka's standout batter this series, as Smith surprisingly reverted to Travis Head's handy offspin ahead of Lyon.
Lyon eventually came on in the eighth over, but it was Kuhnemann who ended Karunaratne's career with the batter prolonging his last moments at the crease with a review in vain. He received an embrace from Lyon and Chandimal before walking off to a big ovation from those at the ground, including the Australians.
Chandimal had scored a couple of 70s in this series, but needed an even bigger contribution if Sri Lanka were to turn around this dire situation. But after being pinned down, Chandimal lost his patience against Lyon and hit to mid-off, where towering Beau Webster moved nimbly to take a sharp catch low down.
Sri Lanka's batters were unable to carry over the momentum after their bowlers had done well to take seven wickets in the first session.
Australia resumed in a powerful position at 330 for 3, but they knew there was work to do in their bid to only bat once in this match. After such a limp performance in the backend of day two, Sri Lanka desperately needed a spark and they immediately took the second new ball.
Carey overtook his highest first-class score of 143 in style with a firm sweep that rocketed to the boundary and he also moved past Adam Gilchrist's 144 as the highest score by an Australian wicketkeeper in Asia.
Jayasuriya was rewarded for his attacking line and lengths when Smith's stout defence was finally breached on 131 by a brilliant delivery that pitched on off stump and gripped off the surface.
Smith walked off immediately after feathering an edge to wicketkeeper Kusal Mendis and he received a rousing ovation, but his dismissal reinvigorated Sri Lanka and brought a different complexion to the game.
Josh Inglis made his way to the crease one spot lower in the batting-order after spending time off the field during Sri Lanka's first innings because of a back spasm.
After scoring a memorable debut ton in the first Test, Inglis found himself in a tougher position and had a nervous moment first ball when only an inside edge saved him from being plumb lbw. But Inglis' stumps were rattled on the next delivery when he played back to a full delivery that skidded on.
Carey on 156 finally succumbed to the sweep, a stroke he had been almost faultless through the innings, when he played over the top of a Jayasuriya delivery and was clean bowled.
All eyes were on 21-year-old debutant Cooper Connolly, who boasted a first-class average of 61.80 from four matches but three of those was at the pace-friendly WACA ground. This was an initiation into Test cricket for Connolly, who was beaten by a sharp offbreak from Nishan Peiris, Sri Lanka's most threatening bowler on day two.
Connolly has proven to be a big-game performer in his fledgling career, backing his aggressive instincts, and he got off the mark in trademark cavalier fashion with a boundary albeit off a top-edge from a full-blooded sweep.
But Connolly didn't add to his tally and was too ambitious when he skipped down to Peiris only to slice to backward point in an ugly dismissal. Webster steadied the situation briefly until being bowled by a big offbreak from Ramesh Mendis as Australia's tail quickly fell away.
