The test and one-day skipper bowled Mahmudullah for two, had Mahedi Hasan caught for a duck by Adam Zampa at deep third man and then dismissed Towhid Hridoy for 40 when the batter scooped to Josh Hazlewood at the Sir Vivian Richards Stadium.
It was Cummins’s first hat-trick in international cricket and also the first of the tournament, which is being co-hosted by the West Indies and United States.
Cummins’s burst of wickets helped Australia restrict Bangladesh to a modest score of 140 for eight in the first innings after the South Asians threatened to mount a big total.
He finished with 3-29 from his four overs after taking a bit of punishment from the Bangladesh batters early on.
Australia will chase 141 for victory after captain Mitchell Marsh won the toss and elected to field first.