Nissanka and Mendis added 170 for the second wicket before Mendis, who was barely able to walk, had to leave the crease having received treatment over the preceding overs. However, any concerns that Sri Lanka's progress would be stalled were eased by Dhananjaya de Silva while Nissanka picked up his rate again after reaching three figures from 123 deliveries to finish with Sri Lanka men's highest individual score against Australia.
Sri Lanka's chase, completed with nine balls to spare, belied what had appeared to be a competitive total from Australia, who overcame mid-innings problems against spin to take 98 from the last 10 overs largely through Travis Head and Glenn Maxwell.
However, in the second half of the game there was a stark difference between the two sets of spinners: where Jeffrey Vandersay, Maheesh Theekshana and, until an expensive final over, 19-year-old Dunith Wellalage were excellent, Australia's combination of Maxwell, Matthew Kuhnemann and Marnus Labuschagne did not provide the same threat.
Australia had opted to leave out their specialist legspinner Mitchell Swepson as they changed the balance of the side to have Cameron Green batting at No. 8 with Pat Cummins rested. Mitchell Marsh, who was returning from his calf problem in place of the injured Steven Smith, did not bowl.
Niroshan Dickwella, back at the top of the order for the injured Danushka Gunathilaka, gave the chase a brisk start before he missed a straight delivery from Maxwell two balls after being dropped by Marsh, who spilled a simple chance at midwicket.
From then on it was all about the second-wicket pair. Mendis has considerable experience under his belt without consistently delivering on his huge talent but, at 27, has time to turn that around while Nissanka is still forging his way in a career that has shown dashes of brilliance.
It was Mendis who was the more free-flowing early on - a brace of drives against Green were especially pleasing - but Nissanka held his nerve. To counter what is frequent criticism of Sri Lanka's white-ball batting, the pair kept the scoreboard ticking with plenty of ones and twos while sensibly respecting good deliveries.
Nissanka produced one of the shots of the innings when he advanced at Josh Hazlewood and deposited him over deep midwicket for six. The chase was barely half done at that point, but Sri Lanka were well in control and never relinquished it.
After Aaron Finch had opted to bat, David Warner departed early when he top-edged a pull. Then it was the 19-year-old Wellalage, whose composure in all facets has stood out in his debut series, broke through when Marsh drove in the air to cover. His opening six-over spell cost just 16 and was chiefly responsible in keeping the pressure on Australia's top order.
There were only two boundaries between the 10th and 20th overs, the second of them when Finch briefly broke the shackles by clumping Vandersay over long-on. Finch's hardworking fifty came from 68 balls as he and Labuschagne built a platform, but it was soon to be dented.
Vandersay's early overs had provided threat without reward; Finch was given a life on 38 when de Silva missed a sharp edge at slip. A perfect legbreak to Labuschagne changed that when the batter stretched out of his crease, then Finch edged another sharply-turning delivery that was brilliantly held, one-handed to his right, as de Silva made amends at slip.
Head and Alex Carey played carefully to begin the rebuild: after a straight six by Carey in the 30th over there was another eight-over period without a boundary. Carey then started to increase the tempo - including taking Theekshana for the only four of his spell - but was lbw sweeping, one short of his half-century.
Then came Maxwell with a brief, but thrilling, display as he unfurled a full range of strokes before he was brilliantly caught by Wellalage running back from mid-on to give Vandersay his third wicket. Head, transferring his form from the top of the order to the middle, went to his fifty amid a late flurry of sixes but a superbly-constructed chase put that in the shade to leave Sri Lanka sensing a notable series victory.
(Except for the headline, this story, originally published by espncricinfo.com has not been edited by SLM staff)