Set a formidable target of 324 in their second innings at Sinhalese Sports Club (SSC), the world number one Test side collapsed in the afternoon session on the fifth day and were all out for 160.
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.
Openers David Warner and Shaun Marsh gave Australia some hope of a consolation win with a brisk start in the morning session but once their partnership was broken, the visitors suffered a rapid collapse.
Herath soon took over from his fellow spinner to dismiss Australian skipper Steve Smith and senior batsman Adam Vogues in the same over.
Warner, who had batted well for his 68 with six fours and a six, was Perera's second big strike.
Herath, who had claimed six wickets in the first innings, then ran through the Australian middle and lower order as the visitors' batsmen had no answer to his left-arm spin.
Earlier Sri Lanka, who resumed on 312 for eight, declared their second innings on 347 for eight with overnight batsman Dhananjaya de Silva unbeaten on 65.
Playing in just his third Test, de Silva smashed 10 boundaries during his 74-ball knock, after scoring a century in the first innings.
Kaushal Silva's gritty 115 played a big part in Sri Lanka registering their first series sweep against a major side since gaining Test status in 1981.
Defiant centuries from Dinesh Chandimal and Dhananjaya de Silva ensured that the hosts get a decent first innings score of 355.
Sri Lanka had only ever beaten Australia once before in a Test match but they won the first two contests of the series comfortably in Pallekele and Galle before wrapping up proceedings in the capital.
The teams now head into the limited-overs phase of the tour with the first of the five one-day Internationals scheduled for August 21.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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