Paceman Ebadot Hossain struck late in the opening session of Day 5 to break a stubborn partnership, leaving Afghanistan at 203 for 4 at lunch with Bangladesh needing six wickets for victory.
After a long, wicketless period for the Bangladeshi bowlers, Ebadot delivered the breakthrough by dismissing Ikram Alikhil, who was caught behind by wicketkeeper-batter Litton Das off a bouncer.
The dismissal ended a crucial 66-run stand between Sediqullah Atal and Ikram Alikhil, which had built up after Hashmatullah Shahidi returned retired hurt.
Following Ikram's departure, Ismat Alam walked out to the crease just before the umpires called for the lunch break.
At the end of 79 overs, Afghanistan reached 203 for 4, requiring another 276 runs for victory, while Bangladesh need 6 more wickets to secure the win.
-SA