Chasing a revised target of 152 for a win under the Duckworth-Lewis method, Jayawardene (61 not out) anchored the run chase with a solid 67-ball unbeaten knock after opener Tillakaratne Dilshan (45) and Kumar Sangakkara (30) laid the foundation for an easy win at the SCG.
Earlier, electing to bat, Australia were all out for 158 in 40.5 overs after the match was reduced to 41-overs-a-side affair with rain interrupting the tie at the end of the 26th over when Australia were 88 for six.
The target for Sri Lanka was revised to 152 and they chased it down in just 24.1 overs, thereby collecting a bonus point also. They needed to overhaul the target in 32.4 overs to get a bonus point.
Sri Lanka got five points (including one bonus point) from today`s win and they now have seven points. All the three teams have played four matches each and India now lead the table with 10 points, ahead of Australia (nine). Each team has two matches left in the series before the finals.
Sri Lanka were in cruise mode from the beginning of the run chase with the openers Dilshan and Jayawardene putting on 74 runs from 11.4 overs before the former was out.
Left-arm pacer Mitchell Starc bore the first brunt of Dilshan`s aggression as the Lankan smashed a short of length delivery over square leg boundary for a six in the fourth over.
Next over, it was the turn of Brett Lee to face the wrath of Dilshan who hit the veteran pacer for three consecutive fours to take 14 runs from the fifth over.
Lee was taken off by stand-in skipper Ricky Ponting and was replaced by Clint McKay and Sri Lankan batsman scored in singles and doubles to quietly reached 66 for no loss after 10 overs.
Dilshan fell in the 12th over to a McKay length ball wide of off stump and the batsman Dilshan threw his bat at it and got a thick edge straight to the slip fielder David Hussey.
Dilshan faced 41 balls and hit four boundaries and a six for his 45. Run rate slowed down a bit after Dilshan`s departure and Sangakkara reached his personal milestone to become the 10th batsman in the world and third Sri Lankan - after Sanath Jayasuriya and Jayawardene - to score 10,000 ODI runs with a single off left-arm spinner Xavier Doherty in the 18th over.
Soon after reaching the milestone Sangakkara punished Doherty again with a four and a six in the same over but two overs later, he fell to Lee caught by Doherty at mid-on while trying for a bit hit.
Sangakkara, who was playing in his 315th match, faced 29 balls for his 30 and hit four boundaries and a six. By the time Sangakkara was out, Sri Lanka were on the verge of victory at 133 for two and they took another three overs to reach the target of 152 which they secured through a leg-bye of Chandimal (six not out).
Jayawardene, who hit his 63rd career fifty today, carried his bat through the run chase, facing 67 balls and hitting five fours.
Earlier, Sri Lanka stifled Australia with a disciplined bowling and fielding display as the home side were shot out for a modest 158. Electing to bat, the Australians failed to stitch any substantial partnership in the face of tight bowling by the Sri Lankans.
But for the 49-run stand between David Hussey (58) and number 10 Mitchell Starc (17 not out) for the ninth wicket, the highest stand in the Australians innings, the total would have been much lower.
David and Starc batted sensibly for eight overs to give some respectability to the Australian innings after their top-order came a cropper to be reduced to 88 for six at the rain interruption. David was, however, fortunate to survive a dropped chance from Malinga when the batsman was on eight.
The Lankans also effected three run-outs as the home side were bundled out with one ball remaining. For Sri Lanka, Farveez Maharoof and Thisara Perera bagged two wickets each for 18 and 29 runs respectively. Malinga, Angelo Mathews and Rangana Herath grabbed a wicket each.
Maharoof, in his return match, used a similar slower delivery to account for stand-in skipper Ricky Ponting (2) who was foxed to an early stroke to give a simple return catch in the 11th over.
Next over, Thisara Perera engineered the run-out of Matthew Wade (15) with a lightening throw to snap the stumps and soon Angelo Mathews joined the party to account for Michael Hussey (13).
Michael Hussey, who returned to the Australian side after being rested from the Adelaide match, was looking good as he hit a six from Mathews but next ball he failed to negotiate a delivery too close to his body and edged behind.
Peter Forrest (16) became the second victim of Maharoof`s tight length and line to offer a catch to the slip and before rain came, Daniel Christian (6) fell lbw to Perera as Australian sauntered to 88 for six.
After the rain break, Clint McKay (3) and Bret Lee (0) fell in quick succession before David Hussey and Starc took the score past 150 with some sensible batting.