The left-arm spinner dismissed Adam Voges, Peter Nevill and Mitchell Starc off successive deliveries to achieve the feat in the second match of the three-Test series at Galle as the visitors folded for 106 in 33.2 overs, their lowest score against Sri Lanka, who grabbed a 175-run first innings lead.
Former paceman Nuwan Zoysa was the first Sri Lankan to claim a Test hat-trick, against Zimbabwe in a 1999 match at Harare.
Herath had troubled Australia in the first Test at Pallekele too, exposing the visitors' vulnerability against spin bowling and claiming nine wickets in Sri Lanka's 106-run victory.
Sri Lanka edge day one with Mendis, Mathews’ fifties
The 38-year-old returned to haunt them again on the second morning, bowling captain Steve Smith for five runs with the first delivery of his third over.
Smith could have been dismissed in Herath's previous over, but Dinesh Chandimal fluffed a regulation stumping chance.
Herath then ripped the heart out of Australia's batting in his eventful seventh over, inducing Voges into a drive with his fourth delivery and Dimuth Karunaratne took a brilliant catch at extra cover to complete the dismissal.
Last session of Australia-Sri Lanka Test washed out
His next delivery was an arm ball that trapped Nevill plumb in front and Herath struck Starc's pad with his next delivery but the leg-before appeal was turned down.
After a brief chat with the spinner, home captain Angelo Mathews decided to review the decision and Herath, who claimed 4-35, was mobbed by teammates as the not-out decision was overturned.
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