But stand-in captain Steve Smith appeared to aggravate his elbow injury in a possible sour post-script to what looks set to be a resounding match and series win in Galle.
Sri Lanka resumed at 8-211, 54 runs ahead of Australia, on Sunday morning and would have been eyeing a lead of 150 to make a game of things on a tough pitch.
But their hopes appeared shot when their last recognised batter Kusal Mendis (50) skied Nathan Lyon (4-84) to Smith, who took his 200th Test match catch in the slips in the first over of the day.
Smith became only the fifth man to take 200 catches in Test cricket, and the first Australian.
Shortly afterwards, Smith appeared to hyper-extend the elbow he injured in the Big Bash League last month as he threw from point.
The skipper had limited his throwing this series by fielding almost exclusively in the slips this series but was throwing to a trainer ahead of play.
He pulled up sore immediately after the throw and tried to shake out the issue as he remained fielding.
But he was in clear discomfort, with Australia's Champions Trophy campaign set to follow the two-match One Day International Series against Sri Lanka.
Australia can ill afford to lose another experienced hand ahead of the Champions Trophy with Pat Cummins (ankle), Josh Hazlewood (side), Marcus Stoinis (retirement) and Mitch Marsh (back) already unavailable.
Beau Webster finished Sri Lanka's innings just before 10.30am local time, crashing into the off stump of Lahiru Kumara (nine) with the part-time spin that had yielded a breakthrough late on day three.
Sri Lanka were all out for 231 in reply to Australia's 414, having been skittled for 257 in the first innings.
Australia are now in the box seat for a first Test series sweep on the subcontinent since their tour of Bangladesh in 2006, and first series win in Sri Lanka since 2011.
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