Kumar Sangakkara became the 2nd Sri Lankan to reach the 10,000-run milestone in Tests, but there was little else for Sri Lanka to celebrate on their first Boxing Day at the MCG since 1995.
Sri Lanka was all out for 156 runs in their 1st innings.
At stumps, Australia was 150 for 3, and they had their in-form captain Michael Clarke at the crease on 20, alongside the vice-captain Shane Watson on 13.
Resuming Day 2, Australian batsmen continued their good form and scored runs at ease.
Captain Michael Clarke was not out on 56 while Shane Watson was on 60 at lunch.
Australia lead by 82 runs with 7 wickets remaining.