The result sees the hosts into the Super Eights while Australia are now on the brink of an early exit and reliant on other results to keep their campaign alive.
Sri Lanla chased down a target of 182 with two overs to spare in Kandy as Nissanka struck 100 from just 52 balls, combining five sixes with 10 boundaries in a composed yet aggressive display that marked the first century of the tournament.
The opener found strong support from wicketkeeper-batter Kusal Mendis, who contributed a steady 51 off 38 deliveries. Their 97-run partnership for the second wicket removed any pressure from the chase before Nissanka accelerated alongside Pavan Rathnayake, who added an unbeaten 28 to guide Sri Lanka comfortably to 184-2.
The knock also saw Nissanka become the first Sri Lankan player to register two T20 international centuries, underlining his growing importance to the side as they continued their perfect start to the tournament with three consecutive wins.
Australia's innings initially promised far more after captain Mitchell Marsh returned from injury and combined brilliantly with Travis Head at the top of the order. The pair blasted 104 runs in just 8.2 overs, putting Sri Lanka firmly on the defensive.
Head struck 59 from 29 balls while Marsh added 54 from 27 in his first appearance of the competition, laying the foundation for what appeared likely to be a total exceeding 200.
However, the innings unravelled dramatically after the openers were dismissed. Sri Lanka's slower bowlers applied pressure through the middle overs, with leg-spinner Dushan Hemantha leading the fightback with figures of 3-37. Australia's aggressive approach backfired as they lost their final five wickets for just seven runs, eventually being bowled out for 181.
The absence of their frontline pace trio further compounded Australia's difficulties, as their attack struggled to contain Sri Lanka's confident batting display.
The defeat leaves Australia needing a sequence of favourable results to progress. Their hopes now rest on the outcomes of matches involving the Zimbabwe and the Ireland. A Zimbabwe victory in either of their remaining fixtures would eliminate Australia from the tournament.
Should Zimbabwe lose both of those matches, Australia would still need a comprehensive win over the Oman while significantly improving their net run rate to sneak into the Super Eights.
Meanwhile, Sri Lanka's victory secures their progression and places them alongside the England in the next round, with other qualification spots still to be finalised as the group stage reaches its conclusion.
For Australia, the result represents a dramatic fall from their status as 2021 champions, with injuries and inconsistency threatening to bring their campaign to an abrupt and disappointing end.
Yuvraj Samra hit a record-breaking century for Canada but New Zealand aced the run-chase to come away with an eight-wicket win to secure their place in the T20 World Cup Super 8s.
England were made to sweat for large parts but eventually showed their metal before beating Italy by 24 runs to book their place in the next round of the T20 World Cup.
Azmatullah Omarzai starred with bat and ball to help Afghanistan register their first win of their T20 World Cup campaign after beating UAE by five wickets with four balls to spare.
Australia have confirmed that Steve Smith has officially been added to their T20 World Cup squad, replacing injured fast bowler Josh Hazlewood.
