It was the third time in a row that the Australians had lost all of their Tests in away series against teams from the sub-continent.
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David Warner is 44 not out, with Marsh dismissed for 23 by a brilliant juggling bat-pad catch from Kusal Mendis off the bowling of Dilruwan Perera.
Sri Lanka were as good in the second innings as they were in the first.
Off-spinner Nathan Lyon, who has claimed two wickets, sent Sri Lankan skipper Angelo Mathews trudging back to the pavilion for 26, ending a 58-run fifth-wicket stand.
He faced 74 balls and hit 10 boundaries to increase the scoring rate.
The fate of the third Test between Australia and Sri Lanka in Colombo can be viewed as a virtual bowl-off between two left-armers.
Dinesh Chandimal and Dhananjaya de Silva, who notched up centuries in the just-concluded Colombo Test, also made significant gains in the Test batsmen rankings.
Australia are unbeaten in home Test series since losing to South Africa in December 2012, but have struggled further afield. But following losses by 106 runs in Pallekele, 229 runs in Galle and 163 runs in Colombo, They have joined England on 108 points but ranked above Alastair Cook’s side, while Sri Lanka have jumped to 95 points.
The teams now head into the first of the five ODIs scheduled for August 21.
As Sri Lanka took a lap of honour around the Sinhalese Sports Club with the fans on their feet, Steve Simth’s Australia looked on wondering just what they are to do to register a Test win in Sri Lanka and the sub-continent.
Sri Lanka’s three comfortable victories came in a flurry after they had beaten Australia only once – in 1999 – in 33 years before this tour.
“This team deserves that (going to number one) for six years of no cricket at home, sometimes people think it’s easy – the UAE suits us, we win – but just getting every day away from the country, without family and friends and all games out of Pakistan, it’s really hard”, Misbah told reporters at The Oval on Sunday after Pakistan won with more than a day to spare.
“Our spinners have done their best to adapt, but I suppose their batsmen have played spin exceptionally well and made it very hard for a spinner to settle”, he said. Credit should go to this man.
The Test team rankings are updated at the end of each series.
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It was his seventh 10-wicket haul in a Test. Herath was named man of the match and man of the series for his tally of 28 wickets.
