With nightwatchman Taijul Islam moving to 55-1, the left-hander almost had Kamindu Mendis caught at slip before a leg-before appeal was turned down.
Sri Lanka ended Bangladesh's stiff resistance when left-arm fast bowler Fernando uprooted Zakir's leg stump.
Captain Nazmul Hossain Shanto looked aggressive from the start and faced 11 balls for his one delivery and was out after attempting an on-drive, which was caught by Dimuth Karunaratne at short midwicket.
Fernando bowled Taijul for 22 runs on another inswing ball, taking Bangladesh's score to 105-4.
Sri Lanka dominated Bangladesh in the first two days and scored 531 runs, the highest Test score without any batsman scoring a century.