Dilshan smashed 106 and Jayawardene 80 to help propel Sri Lanka towards their victory target of 272 with 34 balls to spare and ensure the teams would return to the Adelaide Oval tomorrow to decide the tournament victors.
Michael Clarke earlier scored a superb 117 and David Warner backed up his 163 in the hosts' victory in the first match of the final at the Gabba on Sunday with a more circumspect 100 in a stand of 184 for the third Australian wicket.
The Australians, both hampered by injury, failed to drive home their advantage though, and the tally of 271/6 from 50 overs looked under threat almost from the moment the Sri Lankans came out to bat.
Captain Jayawardene got a lift on one when he was dismissed caught behind by Clint McKay but was called back to the crease after a television review revealed a no ball.
From then on it was plain-sailing and the 100 partnership came up on the first ball of the 16th over as Australia's bowlers laboured and their fielders showed a sloppiness they have avoided for most of the season.
Paceman James Pattinson finally separated the openers when he trapped Jayawardene leg before with an inswinger but by then the Sri Lankans were only 93 runs short of their victory target.
Mike Hussey finally caught Dilshan at deep mid-wicket off the bowling of Brett Lee but Kumar Sangakkara (51 not out) and Dinesh Chandimal (17 not out) comfortably accumulated the remaining 38 runs required for victory.
Sri Lanka, too, had been guilty of sloppy fielding and Clarke was dropped three times as he reached his 17th century in all forms of the game since he became Australia captain last March.
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