Australia's hopeless batting against spin on the sub-continent has claimed another victim, as Steve Smith suffered his first loss in 12 matches as captain.
Australia resumed on 3-83 and was spun out for 161, losing by 106 runs. A big-turning wicket is likely to greet the tourists for the second Test in Galle on Thursday.
It’s Australia’s seventh consecutive loss in away Tests against sub-continental teams.
Veteran spinner Rangana Herath claimed 5-54 and match figures of 9-103.
The jubilant home side’s win was a historic victory at Kandy’s Pallekele Stadium. It came 17 years after Sri Lanka’s only other triumph against Australia at Kandy’s Asgiriya Stadium.
Herath and debutant spinner Lakshan Sandakan dominated the match, taking 16 wickets between them.