The hosts reached their daunting target of 292 to win with nine balls to spare in Colombo and took a 2-1 lead in the five-match series.
Australia chose to bat first and scored 6-291. Sri Lanka finished on 4-292 in 48.3 overs. It was the highest successful run chase at the venue, improving on India’s 5-288 against Sri Lanka in 2012.
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Nissanka shared a 170-run stand for the second wicket with Kusal Mendis (87) before Mendis had to retire with a hamstring injury.
“We knew it was going to be a difficult chase and we needed to keep wickets in hand,” Nissanka said.
“That big partnership with Kusal was crucial.”
Mendis batted beautifully as he has done throughout the series. He played spin expertly with clever use of feet and bisected the field brilliantly. He brought up his half-century in just 39 deliveries, reaching the milestone by pulling Josh Hazlewood for four.
Mendis had raced to 87 off 85 balls with seven fours when he had to be carried off the field.
Nissanka too was limping while running between the wickets, but there was no stopping him as he posted his career-best score before going on to complete his first hundred. He made 137 off 147 deliveries with 11 fours and two sixes.
Nissanka was playing the anchor role and needed 63 deliveries for his half-century. He reached his hundred in 123 balls before upping the tempo with some elegant strokes. By the time he was dismissed, the job was almost done as Sri Lanka just needed eight runs.
It was only the second hundred by a Sri Lankan this year in ODIs.
Earlier, Travis Head posted 70 not out off 65 deliveries with three fours and three sixes. Australia scored 34 runs in the last two overs, including three sixes off Dunith Wellalage’s penultimate over. Head, who batted at No.6, added 72 runs off 80 deliveries with Alex Carey (49) for the fifth wicket.
“Credit to Sri Lanka for the way they batted,” Australian skipper Aaron Finch said.
“I thought the wicket got better under lights.”
Sri Lanka left out opening batter Danushka Gunatilleke, who was nursing a hamstring injury. Niroshan Dickwella came into the side.
Australia made three changes to the side that lost the second ODI at Pallekele.
The tourists’ injury woes worsened with Steve Smith ruled out with a left quadriceps injury. The former captain had been in good form with scores of 53 and 28 in the series. Mitchell Marsh was declared fit, and Australia also brought in Jhye Richardson and Cameron Green in place of Pat Cummins and Mitchell Swepson.
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