Eranga finished with 4-49 and Lakmal claimed 3-66 to help bowl out Bangladesh for 232 after the tourists won the toss and chose to field at the Sher-e-Bangla stadium.
Skipper Mushfiqur Rahim (61) and Shakib Al Hasan (55) were the only batsmen to resist the accurate Sri Lankan attack on an even-paced pitch.
Sri Lanka made 60 for no loss in reply by stumps, with Dimuth Karunaratne unbeaten on 28 and Kaushal Silva on 30.
They are now 172 runs behind with all 10 wickets in hand.
Eranga, who had taken 33 wickets in 10 previous Tests, said the plan to bounce out Bangladesh worked well.
"There was an obvious plan to use the short ball, otherwise it would have been difficult to take wickets on this pitch," he said. "I am glad it went well for me today."
The tourists justified skipper Angelo Mathews' decision to bowl first by grabbing four wickets with just 59 runs on the board.
Shakib and Rahim joined hands at that stage to stitch together a fifth-wicket stand of 86, before the hos