Australia, trailing Sri Lanka by 157 runs on the first innings, were 303-4 in their second knock at lunch on the fifth day of the third and final Test in Colombo on Tuesday.
Skipper Michael Clarke was unbeaten on 71 and Michael Hussey was on 21, with Australia 146 runs ahead with six wickets in hand.
Australia need a draw to win the series 1-0, having taken the first Test in Galle by 125 runs.