Australia claimed six last-session wickets to finally end Sri Lanka's stubborn resistance and seal victory in the first Test in Hobart.
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Mitchell Starc polished off the tail to finish the innings with five wickets, building on Peter Siddle's earlier work, as the hosts clinched a 137-run win by bowling out their opponents for 225.
Sri Lanka had looked like rescuing an unlikely draw when they reached tea on 186 for four but, despite having to battle for almost 120 overs, the Australia attack completed the job just in time.
Starc finished with figures of five for 63 and Siddle with four for 50 to be named man of the match.
Siddle, who came under scrutiny for allegations of ball tampering during Sri Lanka's first innings, struck once in each of the first two sessions of the day, claiming the wickets of Mahela Jayawardene and Kumar Sangakkara (63). The second came immediately before the first of two rain breaks which substantially aided the cause of the tourists, who had long since given up any hope of reaching their target of 393.
As well as the weather, which accounted for the best part of an hour of the afternoon session, Sri Lanka had DRS on their side as technology came to the aid of Sangakkara and Thilan Samaraweera (49) after they were on the wrong end of lbw decisions from umpire Nigel Llong.
But Siddle removed Angelo Matthews and Samaraweera to renew the hosts' hopes before Starc took centre stage.
Having injured his hamstring batting on day four, Australia captain Michael Clarke took the field from the outset, rooted to his place at first slip and no doubt hoping for an early breakthrough to give the home side much-needed momentum.
But there was little encouragement and it came as something of a surprise when Siddle tempted Jayawardene into an open-bladed prod outside off stump that travelled low to Clarke's right at first slip and was duly pouched by the hamstrung captain.
Sangakkara survived a real scare 10 minutes before the break, successfully reviewing a Llong lbw decision that had seen him given out to a shooting Shane Watson delivery angled in from around the wicket. Replays showed the ball hit him outside the line of off stump.
And it was a similar story in the fourth over after lunch when Samaraweera earned a reprieve to another Llong lbw decision, this time off Siddle, which struck the batsman outside off.
Two overs later, DRS was called into action again, but this time there was no reprieve for Sangakkara, who was struck in line by a ball going on to hit middle stump.
The weather immediately took the players off for a break before Mathews and Samaraweera survived two tricky mini-sessions, punctuated by a second rain interruption.
Clarke turned to wicketkeeper Matthew Wade to bowl the last over before tea, with Phillip Hughes putting on the pads and gloves behind the stumps.
The move may have smacked of a measure of desperation from the Australia captain, but it was far from the least threatening over of the day.
The final session proved key, though, as Siddle and Starc turned the match decisively in Australia's favour.
Siddle had Matthews caught behind by Wade, back behind the stumps, for 19, before trapping Samaraweera lbw playing forward.
Starc gave his fellow paceman a helping hand by having Prasanna Jayawardene (21) caught at slip by Michael Hussey.
He then had Nuwan Kulasekara (nine) caught behind by Wade and four overs later bowled Rangana Herath (eight) off an inside edge.
That left the hosts needing one more wicket for victory and it duly arrived two overs later, Wade taking his fourth catch of the innings to dismiss Shaminda Eranga for six and hand Starc his fifth victim.