Bangladesh recovered strongly after slipping to 61 for 3, with Hridoy leading the rescue act through an impressive 83 off 88 balls.
The right-hander shared a crucial 92-run partnership with Litton Das before combining with Mosaddek for another valuable stand worth 93 runs.
Acting captain Najmul Hossain Shanto, leading the side in place of the concussed Mehidy Hasan Miraz, won the toss and chose to bat. However, Bangladesh suffered an early setback when Soumya Sarkar was bowled by Xavier Bartlett for 2 in the opening over.
Tanzid Hasan Tamim made 19 before falling to Matt Renshaw, while Shanto struggled for fluency and was dismissed for 24, leaving the hosts under pressure.
Hridoy and Litton then steadied the innings with a patient partnership. Litton looked set for a landmark half-century at Mirpur before retiring hurt on 48 after suffering muscle discomfort.
With Litton temporarily off the field, Hridoy accelerated and reached his fifty from 62 deliveries. He appeared on course for a century before being caught at midwicket for 83 while attempting a big shot off Ben Dwarshuis.
Musaddek continued the momentum, bringing up his second fifty of the series in just 43 balls. The all-rounder, who had scored 86 in the opening ODI, remained unbeaten on 56 from 51 deliveries.
Litton later returned to the crease and completed his first ODI fifty at Mirpur, finishing unbeaten on 58 from 78 balls. The wicketkeeper-batter had previously played 27 ODI innings at the venue without reaching the milestone.
Bangladesh's total was also boosted by 29 extras, including 18 wides from the Australian bowlers.
Australia now need 275 runs to avoid a series whitewash after Bangladesh secured a historic maiden ODI series victory over the world champions in the previous match.
