The Tigers restricted the Aussies to 121 for seven after the visitors chose to bat. Mustafizur Rahman picked up three and Shoriful Islam grabbed two in the 5-wicket victory at the Sher-e-Bangla National Cricket Stadium on Wednesday.
The pitch, although a different one, was once again slow but looked otherwise when Starc had the new ball in hand.
Bangladesh's chase of a small target wobbled midway with Shakib Al Hasan and Mahmudullah back in the hutch. But youngsters Afif Hossain (37) and Nurul Hasan (22) rose to the occasion and got Bangladesh over the line with an unbeaten 56-run stand.
He paired up with Shakib (26) for 37 to steady the ship, but quick strikes from Andrew Tye, Adam Zampa and Ashton Agar reduced Bangladesh to 67 for five in the 12th over.
Afif and Nurul then took control and kept their calm. After getting an lbw decision overturned when he was on 1, Afif showed composure and began to work the ball around watchfully, occasionally finding boundaries.
After Afif bludgeoned Tye for a six to bring the required run below six per over, the duo regained confidence and began stroking the ball harder, smashing boundaries to eventually coast to the win with eight balls to spare.
He and Shoriful took 5 for 50 between themselves, as the youngster supported Mustafizur well from the other end.
A 57-run stand for the third wicket between Mitchell Marsh, who once again put up a 45-run resistance, and Moises Henriques (30) set up Australia for a launch later in the innings.
But Bangladesh bowlers tipped the balance in their favour after Henriques was removed by Shakib in the 15th over.
Marsh soon edged behind to dim the Aussie hopes of a late burst as his team managed to add just 31 in the last five overs for the loss of four wickets.
“Losing a few early wickets caused tension in the dressing room, but the way Afif and Sohan (Nurul) batted, it was a lot of relief. I think Mustafizur has always been there in these conditions, and effective too.
“Shoriful bowled really well and all the bowlers chipped in too. We are taking it game by game."
The team will face in their third ODI on Friday.