Australia lost Warner at the score of just two runs on the board as the left arm batsman was bowled by Rangana Herath after contributing just one run from four deliveries.
Australia were set a target of 268 to win the rain-hit first Test after bowling out Sri Lanka for 353 in their second innings on the fourth day in Pallekele Friday.
Sri Lanka, 282 for six overnight, lost top run-scorer Kusal Mendis (176) in the morning session, which lasted for just 45 deliveries due to rain and bad light.
Number nine batsman Rangana Herath then offered some good resistance with his 34-ball 35, including six boundaries, to frustrate the visiting bowling attack in a game which looks evenly balanced.
Australian pace spearhead Mitchell Starc, who took the prized wicket of Mendis, led the charge with four wickets as new ball partner Josh Hazlewood and off-spinner Nathan Lyon bagged two apiece.