Sri Lanka lost five wickets for just 46 runs in the final session as Australia took control of the game.
Sydney: Sri Lanka face a struggle to avoid a series whitewash against Australia after finishing day three of the third and final Test on 225 for 7 in their second innings, just 87 runs ahead.
Wicketkeeper Matthew Wade's unbeaten 102 before lunch helped Australia to a first-innings 432 for 9 declared at the Sydney Cricket Ground.
Sri Lanka started their second innings strongly, but the loss of five wickets for 46 runs after tea turned the match firmly back toward the home side.
Sri Lanka still had hope of a first ever Test win in Australia while Dimuth Karunaratne and Mahele Jayawardene were at the crease but Karunaratne edged Jackson Bird to Wade for 85 to start the slump.
The dismissal of Jayawardene for 60 made it 178-6 and exposed the inexperienced Sri Lanka tail.
Six wickets in the final session and a likely quick mopping-up of the tail on Sunday should allow Australia to push for a 3-0 series victory. However the SCG is notoriously difficult for sides batting last. The highest fourth-innings winning total at the ground is 288.
Australia resumed the day on 342-6 in response to Sri Lanka's first innings of 294, and Wade and Peter Siddle added another 42 runs together to take their seventh-wicket stand to 77.
Siddle raced from his overnight 16 to 30 at the rate of a run a ball and made his highest score of the summer (38) before he was deceived by a bouncing delivery from Nuwan Pradeep and was caught behind by Dinesh Chandimal.
Rangana Herath trapped Mitchell Starc (2) leg before wicket and bowled Nathan Lyon for 4, finishing with 4-95, but Wade kept throwing his bat at anything hittable to keep the scoreboard rolling.
Wade reached his century with his ninth four and ran halfway to the boundary in celebration, leaping and swinging his bat in the air. Bird had to run after him to congratulate his teammate.
It was Wade's first century since his 106 against the West Indies in Dominica in April last year and his first in Australia.
Wade and Jackson Bird (6 not out) put on 39 from 31 balls in an unbroken last-wicket partnership before Australia declared.
Karunaratne and Jayawardene guided Sri Lanka to 130-1 at tea for only the loss of Tillakaratne Dilshan; the opener edging Mitchell Johnson to Phil Hughes in the slips for just 5.
Sri Lanka needed a big contribution from captain Jayawardene, who was averaging just 33.06 over the past two years against a career average 49.62.
Mindful of his team's predicament, Jayawardene played conservatively but Karunaratne, in only his fourth test, reached his second international half century with a huge six to long on from Lyon, reaching the mark off 71 balls.
The promising platform they had built started to disintegrate when Bird got the ball to swing away from Karunaratne and the left-handed opener touched the faintest of edges to wicketkeeper Wade, precipitating a succession of wickets.
Lahiru Thirimanne successfully challenged an lbw verdict but went soon after for just seven, caught by Bird off the bowling of Johnson.
Jayawardene was left with his hands on his hips in frustration as 155-3 became 158-4 when Thilan Samaraweera (0) recklessly heaved a Lyon delivery to Mike Hussey, leaving him with a tour average of 13.16 and giving the home crowd another chance to celebrate Hussey in his final test.
The biggest cheer of the day came when captain Michael Clarke gave Hussey a bowl just before the close.
Angelo Mathews scored four boundaries for his 16 runs before he was run out by David Warner's smart throw following a mix up with Jayawardene, and 178-5 became 178-6 when Jaywardene was caught at first slip off Siddle by Clarke.
Dhammika Prasad and Dinesh Chandimal put on 24 for the seventh wicket before Prasad was caught behind off Starc for 15. Chandimal made his way to 22 not out by the close, with Rangana Herath unbeaten on 9.
After six wickets in the final session, Australia's batsmen should not have to worry too much about the Sydney Cricket Ground, where wickets have traditionally hindered sides batting last in tests. Australia's
288-2 against South Africa in 2006 is the highest winning fourth-innings total at the SCG.
Wade added 55 to his overnight score to help Australia to a 138-run first-innings lead and delight the fans, the majority of whom were wearing pink in honor of the cancer charity set up by Australia great Glenn McGrath and his wife, Jane, who died of the disease in 2008.