The upset over the No.1-ranked Test side marks a big turnaround for No.7 Sri Lanka, who went into the match with an inexperienced XI - including two debutants - and followed a dismal tour of England, where they were thrashed 2-0.
Aside from Herath's match figures of 9-103, 21-year-old Kusal Mendis was the hero for the home side when his stunning 176 on day three hauled them back into the game after they were rolled for just 117 in 34.2 overs on Tuesday.
His haul helped Sri Lanka to a second-innings total of 353 and set Australia a target of 268, which was a tall order given the visitors' recent struggles on subcontinental pitches.
Australia's poor record of chasing large totals in the region is stark - in 14 attempts their only successful Test run chase above 200 was when they made 307 against Bangladesh in 2006 in Dhaka.
That's not to take anything away from Sri Lanka's well-balanced slow-bowling attack led by 38-year-old Herath and complemented by exciting left-arm wrist spinner Lakshan Sandakan, who took match figures of 7-107 on debut, and right-arm offie Dilruwan Perera.
Smith was out just before lunch for 55 when he was lbw to Herath to just about end any hopes of an Australian victory after they had resumed in the morning at 3-83.
Smith was given caught behind not long after he had become the first Australian to score a half-century in the match, but was reprieved on review.
However, the captain soon after played down the wrong line to a Herath delivery and was trapped in front lbw.
Mitch Marsh hit some powerful drives in his 25 but was also lbw to Herath.
The 71-Test veteran also accounted for Adam Voges (12) in a bizarre caught-and-bowled that at first looked like a bump ball but was shown to be a fair catch by the TV match official.
Poor weather became Australia's friend after each of the first four days were affected by rain or bad light.
- AAP
