The hosts, bundled out for 117 in the first innings, lost opener Kusal Perera to fast bowler Mitchell Starc when rain forced an early tea and eventually the second day’s play was called off.
Kaushal Silva was batting on two with Sri Lanka still 80 runs behind in the bowler-dominated first match of the three-test series.
Earlier, the local spin duo of veteran Rangana Herath (4-49) and debutant Lakshan Sandakan (4-58) shared eight wickets between them to keep Sri Lanka in the contest despite their capitulation in the first innings.
Resuming on 66-2, Australia lost both the overnight batsmen to Herath who quit limited-overs cricket in April to focus on the longest format of the game.
Australia skipper Steve Smith (30) threw his wicket away in the second over of the day, dancing down the track to try and slog the left-arm spinner only to miss the line and be stumped.
Herath returned to dismiss Usman Khawaja (26) in his next over, trapping him leg-before with a turning delivery.
Adam Voges (47) survived a vociferous leg-before appeal in the very first delivery he faced from Herath but went on to make the highest individual score so far in what appears to be a low-scoring match.
Mitchell Marsh (31) ran hard between wickets and helped himself to five boundaries before becoming left-arm Chinaman bowler Sandakan’s maiden test victim.
Paceman Nuwan Pradeep, who had dismissed Australia opener David Warner for a duck on Tuesday, claimed the crucial wicket of Voges.