"We have been outplayed in every facet of the game," a glum Australian skipper Steve Smith told reporters.
"It's been a very tough series again.
"That's the our third straight whitewash loss in the subcontinent. What we are doing isn't working."
The capitulation was Australia's ninth straight defeat in Asia following a 2-0 loss to Pakistan in 2014 in the UAE and 4-0 hammering in 2013 at the hands of India.
Australia produced another woeful batting display in the run chase, again failing to cope with the home side's spinners to be skittled in just 44.1 overs.
The wearing pitch took turn and was difficult to bat on, but it didn't justify another collapse of 5-23 in 39 balls not long after lunch when they were motoring along at 1-77.
Herath was again at the forefront for Sri Lanka.
He snared 7-64 to finish as top wicket-taker for the series with 28, a gutsy display from the 38-year-old who had been limping since late on day two after being hit in the groin by a Josh Hazlewood delivery.
His match figures of 13-145 were also the best by a Sri Lankan in Tests against Australia, bettering Muttiah Muralitharan's 2004 feat of 11-212 in Galle.
Herath was named man of the match and man of the series.
"The feeling in the whole dressing room is unbelievable," said Mathews.
"Regardless of them having a bad record in Asia, they're still the No.1 team and, to beat them, it has to be a fantastic effort."
Dilruwan Perera contributed with 2-71, his dismissal of David Warner - who was bowled around his legs without playing a shot - summing up Australia's mental state to the hosts' clever slow bowlers.
Herath and Perera opened the bowling and offspinner Dhananjaya de Silva, who accounted for four overs, was the only other bowler required.
Warner top-scored for Australia with 68 from 94 balls, while Shaun Marsh (23), Mitchell Starc (19) and Lyon (12) were the only others to get into double figures.
- AAP
