The 20-year-old right-arm paceman collected three more wickets on Tuesday after dismissing the Caribbean opener Wavell Hinds on the first day. It was the first time Bangladesh had dismissed any Test opponents for fewer than 300.
Daren Ganga (63) and skipper Ridley Jacobs (59) hit half centuries to lead a West Indies recovery after the tourists had resumed at 38 for one in reply to Bangladesh's 194.
Ganga struck 10 boundaries from 106 balls with 10 fours before he hit part-time spinner Sanwar Hossain straight to Baisya at mid-wicket.
Jacobs
Manjurul Islam made an early breakthrough, sending back Ramnaresh Sarwan (17) caught behind from a delivery with a little extra bounce.
Shivnarine Chanderpaul went for 16 when he chased a delivery down the leg side and was caught by Bangladesh skipper Khaled Mashud.
Marlon Samuels, who hit a straight six in his brisk innings of 31, attempted a pull shot but succeeded only in lofting a catch.
