Sri Lanka struggling to avoid series whitewash against Australia
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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.
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