After Australia were all out for 203 in reply to Sri Lanka's first innings total of 117, the hosts then lost opener Kusal Perera for just four when he was ruled out lbw to a ball from paceman Mitchell Starc.
Earlier, Australia went on to make 203 runs in their first innings, taking what could prove to be a crucial lead of 86 runs in a low-scoring match.
Adam Voges top-scored for the Australians with 47, meaning no player from either side managed to score a half-century in the first innings.