Glenn Maxwell smashed 145 not out off 65 balls, including nine sixes and 14 fours, to propel the touring side to a score of 263 for three, beating Sri Lanka’s 260 for six against Kenya in 2007.
Australia’s world record was set a week after England plundered 444 for three against Pakistan, the largest team total in an ODI.
Travis Head lifted a leg-side full toss from Thisara Perera for six to beat the record after Maxwell, opening in place of the injured Aaron Finch, flayed his maiden T20 international century.
Maxwell’s knock was the second highest individual innings in a Twenty20 international, behind only Finch’s 156 against England in 2013.
Australia fast bowlers Scott Boland and Mitchell Starc picked up three wickets each as Sri Lanka subsided meekly to 178 for nine, Dinesh Chandimal top-scoring with 58.
The teams meet in the second and final Twenty20 game on Friday in Colombo.