Travis Head (4/10) and Nathan Lyon (4/31) destroyed Lankans in the third innings with their spin, skittling them out for 113.
The first session of play was washed out due to rain.
Lyon leads bowlers day out as Australia bowl Sri Lanka out on day one.
India to tour New Zealand for white-ball series post T20 World Cup. Next year NZ host Sri Lanka for full series.
Day-night Test returns as New Zealand announce busy summer schedule.
Kamil Mishara, Kamindu Mendis and Suminda Lakshan though failed to make the cut.