Australia, who start the Ashes series at the end of the month, never looked like reaching their initial victory target of 244 in 39 overs or the 240 in 38 overs they were handed under the Duckworth-Lewis method after rain stopped play for a third time.
Impressive opener Upul Tharanga contributed an unbeaten 86 to Sri Lanka's 213 for three, which they achieved in 41.1 overs as showers interrupted the action for a total of nearly three hours.
Shane Watson (40), Cameron White (35) and Steven Smith (33) offered the faintest glimmer of hope for the Australians but it was always going to be an uphill battle and they crumbled to 210 all out.
The attendance of 11,495 was the lowest crowd for a one-day international at the Sydney Cricket Ground for 27 years and most was supporting Sri Lanka.
Earlier, the Sri Lankan top order put in a solid afternoon's work to set up the win after relying on the tail enders to produce Wednesday's remarkable victory in the first match in Melbourne.
Australia again labored in the field with Test strike bowler Mitchell Johnson the target of some big hits and Michael Clarke and Watson conspiring to mess up a simple run out.
Tharanga was stranded when Clarke fielded a slow lob from Brad Haddin with plenty of time but he threw the ball straight into the leg of Watson, who was standing in front of the wicket, and the batsman scurried to safety.
Watson was the best of the Australian bowlers, accounting for Kumar Sangakkara, who was caught on the boundary by Clint McKay for 45, and Mahela Jayawardene, who was adjudged lbw for five.
Tillakaratne Dilshan put on 98 for the first wicket with Tharanga before being trapped in front by recalled spinner Nathan Hauritz for 47. The third and final match of the series takes place on Sunday in Brisbane, also the venue for Australia's first Ashes Test against England starting on Nov. 25.
