He is playing his first tournament since suffering serious injuries in a car accident in December 2022 that kept him out of last year's IPL as well as the 50-overs World Cup in India
Skipper Mushfiqur Rahim top-scored for the hosts with 31, while Nathan Lyon (6-60) was the pick of the Australian bowlers, claiming a career-best match haul of 13 wickets.
Bangladesh won the first test in Dhaka by 20 runs.