Australia won its first Twenty20 match since claiming the World Cup last November in the United Arab Emirates.
The hosts defeated Sri Lanka by 20 runs in a solid victory in the first clash of a five-game series.
Despite an underwhelming performance with the bat, Australia's bowling unit was crucial to obtaining the result.
Ben McDermott continued his strong form with a half-century, but the home side ultimately finished with a score of 149-9 after losing the toss.
The target score for Sri Lanka was adjusted to 143 due to rain interrupting play, with Australia comfortably defending the total thanks to two stand-out bowling performances.
Hazelwood marked his return to the international stage with figures of 4-12 from his four overs, which is his career-best Twenty20 international figures.
Spinner Adam Zampa also took 3-18, claiming key early wickets before Hazelwood sealed the win with some late dismissals.
Too good from Zampa 🔥 He takes his third!
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Speaking after the match, Australian captain Aaron Finch felt that bowlers stepped up to secure a result.
"I thought we had to bowl well to defend that total on this wicket, it wasn't the easiest wicket to bat on," Finch said.
"We probably left ourselves a bit short with the bat and got ourselves in a position where we might've been one wicket down too much from probably the 12th over onwards.
"An unbelievable performance from our bowlers."
The second match of the series will be played on Sunday in Sydney before games are held in Canberra and Melbourne.