Kushal Perera and Tillakaratne Dilshan too the visitors off to a good start adding 46 runs for the opening wicket in 38 balls.
Glen Maxwell took a couple of wickets to bring Australia back into the game. However steady batting by Angelo Mathews and Lahiru Thirimanne put Sri Lanka in a comfortable position.
Earlier, Warner remained unbeaten on 90 as Australia set a 138-run target. Electing to bat first, Australia scored 137 in their allotted 20 overs, losing three wickets.
Warner struck three sixes and five boundaries to score a quickfire 90 not out, which came from 62 balls.
Nuwan Kulasekara continued his good form with the ball, taking 1-21 off his four overs.
Australia's middle-order failed against a disciplined Sri Lanka bowling attack, as Aaron Finch and skipper George Bailey failed to make a mark, scoring one and 11 respectively.