Kurtis Patterson smashed his maiden Test hundred Saturday before Australia declared in a commanding position.
Joe Burns was dismissed for 180 but there was little else to cheer about for Sri Lanka with Kurtis Patterson nearing his maiden ton.
Australia threw a surprise when they picked Kurtis Patterson for the first Test against Sri Lanka at Gabba despite not being part of an initial squad of 13.
Pat Cummins got Dimuth Karunaratne off the last ball of day two to give Australia lift.
Travis Head and Marnus Labuschange put on 166 for the fifth wicket.
Sri Lanka have brought in batsmen Lahiru Thirimanne and Dhananjaya de Silva for the first of the two-Test series.
Patterson scored centuries in both innings playing for the Cricket Australia XI against Sri Lanka in Hobart last week.
Australia have named batsman Kurtis Patterson and fast bowler Jhye Richardson in their playing XI for the first Test in Gabba against Sri Lanka that starts from Thursday.
Australia's skipper has stated that his pace attack will have to deliver on a lively track.
Wade said he was previously told by Hohns he wasn't gaining selection because he batted too low in Tasmania's order.