Kusal Perera hit a 25-ball 24 before being caught by Nevill off spinner Holland, with Australia successfully appealing to the video review after he was initially given not out.
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The world number one side, gunning for a consolation win after losing the first two matches, were 77 for one at lunch, needing another 247 runs for victory.
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.
De Silva and Chandimal, who scored 194 and 175 runs in the match respectively – had to absorb huge pressure (that of falling wickets) in both innings.
The 38-year-old Herath took seven for 64 in Australia’s second innings of the third and final Test, finishing with 13 wickets in the match, to confirm his status as the outstanding player of the series.
Sri Lanka made 355 runs in its first innings and Australia made 379. It took Sri Lanka all of 44.1 overs to bundle the beleaguered Australians for 160.
Sri Lanka, who completed a 3-0 whitewash over Australia in a home series on Wednesday, are in sixth position at 95 points.
Silva was unbeaten on 32 with skipper Angelo Mathews on four at the Sinhalese Sports Club.
The teams now head into the first of the five ODIs scheduled for August 21. He had a groin strain so he could not run or jump and on one leg he was fantastic, one leg was enough for him on these pitches. He was fantastic with one leg. “The credit should go to Dhananjaya de Silva and Dinesh Chandimal, the way they got us through the second and third sessions was fantastic and once again Rangana Herath doing his thing”.
Australia had arrived in Sri Lanka as the top Test team with 118 points to play the three-match Test series. “He has been a great team man as well”, Mathews said after the end of the third Test.
“If we have a really good target over 350 or something we put them out of the game”, Silva said.
Sri Lanka first won their series win against the Ausssies back in 1999 with the result 1 – 0.
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Australia’s loss in Colombo was their ninth consecutive Test defeat in Asia, a record that augurs exceptionally poorly for their four-Test tour of India early next year.
