Australia comfortably defended a Duckworth-Lewis-Stern adjusted target score of 143, with spinner Adam Zampa (3-18) inflicting early damage before Hazlewood iced the game with late wickets.
The tourists ended on 122-8 after 19 overs, with the chase reduced after rain interrupted in the 15th over.
The Sri Lankans struggled to adjust to the pace of the wicket, with opener Pathum Nissanka (36) making the only meaningful contribution before being caught off Zampa.
“I thought we had to bowl well to defend that total on this wicket, it wasn’t the easiest wicket to bat on,” said Australia skipper Aaron Finch.
“It was pretty clinical with the ball.”
The home side, playing their first white-ball international since winning the T20 World Cup in Dubai last November, were sent in to bat after losing the toss.
Ben McDermott struck three sixes in his knock of 53, combining with debutant Josh Inglis (23) to lay a solid foundation for Australia.
From 75-1 after 10 overs, the middle and lower-order faltered but Marcus Stoinis scored a quick 30 to ensure a competitive total of 149-9.
The world’s top-ranked T20 bowler, leg-spinner Wanindu Hasaranga (3-38), had mixed fortune with his low-release round-arm variation, conceding multiple boundaries but also accounting for Glenn Maxwell who holed out for seven.
Seamer Binura Fernando was the most economical of Sri Lanka’s bowlers with 2-12 from four overs.
“We didn’t get any partnerships going from the start … (so) we should come up with a better plan for the next game,” said Sri Lanka captain Dasun Shanaka.
The hosts have experienced a tumultuous month in which the men’s team went from winning the Ashes to unceremoniously parting ways with head coach Justin Langer, who resigned citing a lack of support from senior players.
The second match, on Sunday, will also be played in Sydney before the series moves to Canberra and Melbourne.
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