Sri Lanka need another 249 runs to win the first Test match against Australia at Hobart.
The visitors have headed into lunch on the fifth day on 144-3 in their second innings, with Kumar Sangakkara unbeaten on 58 runs.
Thilan Samaraweera is alongside the 35-year-old on the crease and has scored 17 runs from 41 balls so far.
Mahela Jayawardene was the only casualty of the morning session for Sri Lanka, getting dismissed for 19 runs from 77 deliveries.