Tamim, Mahmudul drive Bangladesh to 157-0 at lunch in Sri Lanka Test
The hosts reached 157-0 at lunch after they began the day on 76-0 in response to Sri Lanka's 397 in Chittagong.
Bangladesh trail by 240 runs after Tamim, on 89, and Mahmudul, on 58, kept the Sri Lankan bowlers at bay in the first session despite a few close calls.
Mahmudul, a 21-year-old playing only his fifth Test, survived a reprieve on 51 when Lasith Embuldeniya dropped a catch at fine-leg off Asitha Fernando.
Tamim, unbeaten on 35 overnight, led the batting charge for Bangladesh, hitting 10 fours.
He started the day confidently dispatching left-arm quick Vishwa Fernando for two fours in the second over of the day before bringing his 32nd Test fifty off 73 balls with a boundary.
Mahmudul, who was batting on 31 overnight, was relatively sedate before he completed his second Test half-century in 110 balls when he flicked Asitha Fernando towards mid-wicket for a double.
Sri Lanka suffered a further blow as Vishwa Fernando, having bowled in the morning, was ruled out of the Test after a blow he received on the helmet on Monday. Kasun Rajitha joined the squad as concussion replacement.
Angelo Mathews had held the Sri Lankan innings together before agonisingly falling on 199.
Off-spinner Nayeem Hasan claimed 6-105 for Bangladesh.