Opting to bat first, Australia were all out for 74 runs in 26.4 overs with only Mitchell Starc (22 not out) and Xavier Doherty (15) managing double digits.
For Sri Lanka, Nuwan Kulasekara claimed a career-best five for 22 runs while Lasith Malinga bagged three for 14.
Sri Lanka wobbled early in their chase before reaching 75 for six in 20 overs.
Kushal Perera joined top-scored for the tourists with an unbeaten 22, while Tillakaratne Dishan also contributed as many runs.
Mitchell Johnson was the most successful Australian bowler, claiming three for 11.
Sydney hosts the fourth one-dayer on Sunday.