The Tigers were 96 for 3 in 28 overs at the stroke of lunch. Tamim was batting on 33 with Shakib on 48 at the other end in a partnership worth 86 on Sunday.
After Mushfiqur Rahim elected to bat with the sun shining down at Mirpur’s Sher-e-Bangla National Cricket Stadium, Bangladesh suffered an early collapse as Cummins dazzled with the new ball.
Soumya Sarkar (8) was dismissed first, edging one low to the slips from close to the body. Cummins then took out Imrul Kayes and Sabbir Rahman, both for ducks, to leave Bangladesh tottering on 10 for 3.
Tamim and Shakib, either of whom are playing their 50th Test, then dug deep played through the initial overs.
With Shakib playing his strokes at one end, Tamim looked defensively solid at the other. But the two sixes that Bangladesh had in their account came from the openers bat as he blasted offspinner Nathan Lyon over extra cover on both occasions.
Lyon produced significant turn and bounce through his 11 overs in the first session but got no rewards.
Shakib struck seven boundaries in 62 balls so far.
There was heavy rain overnight in Mirpur but the skies cleared since the break of dawn. This the first game at the ground since the outfield was revamped.
Nasir Hossain is playing a Test after a two years while pacer Shafiul Islam also returned to the fold.
Top order batsman Mominul Haque did not make the cut while Liton Kumar Das was also left out, meaning Mushfiqur will stand behind the wickets. The Tigers are playing with two seamers and a three-pronged spin attack.
The Aussies are playing a Test in Bangladesh after 11 years. Their captain Steve Smith disclosed the lineup in the press conference on Saturday.
Usman Khawaja returned to the team while Ashton Agar will be playing a Test after four years.