Australia were set a victory target of 141 runs after bowling Sri Lanka out for 278 in their second innings before lunch on the fourth day of the third test on Sunday.
The tourists, already 2-0 down in the series, resumed on 225 for seven looking to bulk up their lead of 87 to somewhere between 150 and 175 to give their bowlers something to work with.
Dinesh Chandimal hit a defiant 62 not out off 106 balls but ran out of partners when Jackson Bird had Nuwan Pradeep caught behind for nine about 30 minutes before lunch.
Rangana Herath had survived an early run out scare when Matthew Wade threw the ball over the head of Mitchell Johnson but was gone for 10 in the next over when he dragged the ball onto his stumps off the bowling of Jackson Bird.
Suranga Lakmal did not hang around for long, departing for a duck after walking across his stumps, swinging and missing and watching Johnson's delivery shatter the stumps.
Australia won the first test in Hobart by 137 runs and the second by an innings and 201 runs inside three days in Melbourne last week.