Trailing 2-1 going into the match, Australia needed to win at the SCG in order to level the series ahead of the final match in Hobart on Wednesday.
But after posting a disappointing 222 for nine, rain brought an early end to proceedings with Sri Lanka's reply on 14 without loss off 3.2 overs. The rain had stopped when play was abandoned because of a wet outfield.
David Warner struck an impressive 60 and Mitchell Starc contributed a quickfire 52 not out, but two howlers from the umpires cut short Warner's impressive knock and that of Moises Henriques.
Nuwan Kulasekara had Phillip Hughes out early on edging to wicketkeeper Dinesh Chandimal for one. Australia captain Michael Clarke (20) lost his wicket in the 10th over as Kulasekara (three for 30) secured his second scalp by trapping him lbw. David Hussey did not last long, caught by Lahiru Thirimanne for one off Lasith Malinga (two for 33).
Just as George Bailey and Warner looked to have formed a decent partnership, the former came down the pitch and tried to hit Rangana Herath (two for 37) over the top, sending the ball straight to Thisara Perera at mid-on on 22.
Warner continued his good work in the middle, reaching his half-century off just 57 balls, including five boundaries but was given out to a hugely dubious lbw decision. Replays showed there was a massive inside edge onto his pads off Perera's delivery, but Warner was unable to refer the decision as Clarke had used up the one and only referral earlier in the innings.
Just two overs later Henriques (three) suffered the same fate as the opener. Umpire Paul Reiffel gave Henriques out lbw to Herath, but replays again showed a big inside edge onto his pads.
Matthew Wade was joined by Mitchell Johnson when Australia were 130 for six but the latter exited for 10 after a full, slanting Malinga delivery caught him plumb on his pads for 10. A good innings from Wade (31) came to an end when the wicketkeeper slashed a Perera delivery straight to Kulasekara, who ran in from the boundary to take the catch.
Australia's lower order of Clint McKay (two) and Xavier Doherty (10 not out) did not offer much resistance, but a well-played 52 off just 37 balls by Starc helped the home team to a competitive total.