Mostary, 24, made a magnificent 118 off 134 deliveries and with her captain Nigar Sultana (74no off 114) added 195 for the fourth wicket - the highest partnership against Australia in women's ODI history.
It was also the largest stand for any Bangladesh wicket in women's ODIs and was the foundation of the team's 6-220 off 50 overs,.
Bangladesh's total after being sent in might still not prove enough to challenge Australia but it was achieved with immaculate strokeplay, tactical nous and plenty of courage.
The two Bangladesh heroes came together with their side desperate at 3-8 in the eighth over and embarked on their rescue mission with class.
Mostary brought up her fifty with a cut shot off legspinner Alana King after driving her through cover with panache to the fence.
She earlier struck three exquisite boundaries through the offside in leggie Georgia Wareham's first over.
Mostary now holds the record for the highest all-time score by a No.5 against Australia in women's ODI history, the best by a Bangladesh batter, and the equal-highest at Allan Border Field.
Sultana was strong off her legs, with two immaculate flicks to the fence with perfect balance a highlight. She played the perfect foil to Mostary.
Australia quick Megan Schutt (4-36) was the pick of the bowlers, including ending Mostary's epic knock when she struck her leg stump.
Veteran Bangladesh opener Fargana Hoque (0) has faced two deliveries from Schutt in this series and lost her wicket both times.
Fellow opener Sarmin Sultana (five) was trapped in front after quick thinking wicketkeeper Beth Mooney called for DRS when bowler Kim Garth was unsure.
An inswinging yorker by Schutt accounted for Sharmin Akhter (0) and the visitors were in all sorts in the eighth over.
Australia sent Bangladesh in for the second time in the ODI series as they believed rain may have impacted the run chase.
Captain Tahlia McGrath had no hesitation in making the call when she won the toss on Sunday.
"We reckon there is a bit of weather on the way," she said.
Skipper Sultana was not disappointed by McGrath's call.
"We wanted to bat," she said.
Both sides were unchanged from Friday's opening match of the three-match series, which Australia won by seven wickets.
15°C