Leading Australia's three-pronged spin attack with the new ball in hand, Lyon claimed three wickets in the morning session and another soon after lunch to reduce Bangladesh to 85-4 at the Zahur Ahmed Chowdhury Stadium.
Sabbir and Mushfiqur arrested the slide with a 105-run stand for the fifth wicket. Sabbir fell after tea but Mushfiqur was batting on 62 at stumps with Nasir Hossain on 19.
Desperate to level the series after being humbled inside four days in Dhaka, Australia went in with three spinners and a lone paceman in Pat Cummins, a strategy they had not employed since 1978.
Lyon was rewarded for his clever change of pace, and the Bangladesh batsmen paid the price for playing him on the back foot with the ball often keeping low.
Mushfiqur won an important toss and unsurprisingly opted to bat against a spin-heavy Australian side but the hosts did not get the start they were looking for.
Opener Tamim Iqbal looked uncomfortable against Cummins' pace and was spilled in the slips by Glenn Maxwell. Lyon ensured it did not really matter, however, trapping the opener lbw for nine with a quicker delivery.
Four overs later, Imrul Kayes fell in the same fashion after Australia successfully reviewed the original not-out decision. Soumya Sarkar added 49 runs with Mominul Haque but Bangladesh suffered another setback on the stroke of lunch.
Lyon sent down a skidding delivery to dismiss Soumya for 33 and returned after the interval to claim Mominul for 31, the fourth successive lbw decision. Ashton Agar took the important wicket of Shakib Al Hasan, the architect of Bangladesh's thrilling 20-run win in Dhaka, for 24 with under-fire Matthew Wade taking a fine catch behind the stumps.
Sabbir was not afraid to play his shots and stepped out to hit Lyon for a six in his belligerent 66 before Wade effected a smart stumping to give Lyon his third five-wicket haul in successive Tests. Mushfiqur was his usual composed self at the other end as he brought up his 18th Test fifty.
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