Rashid Khan took three wickets as Afghanistan inched closer to victory against Bangladesh on the fourth day, in the one-off Test, in Chattogram, on Sunday.
Set a huge 398 for victory, Bangladesh were tottering on 136 for six when rain ended play early on Day 4.
The hosts still need another 262 runs for victory on the fifth and final day.
Their hopes largely rest on senior pro Shakib Al Hasan, who stroked his way to a fluent 39, while Soumya Sarkar was yet to get off the mark.
It was Afghanistan captain Rashid, who once did the damage with the ball, taking 3/46, to take his tally to eight wickets in the match so far.
Earlier, opener Ibrahim Zadran top-scored with 87, while Asghar Afghan (50) scored his second fifty of the match to lift Afghanistan to 260 in their second innings.
Rahmat Shah's 102 and Afghan's 92 had helped Afghanistan post 342 in their first innings after they had elected to bat. Leg-spinner Rashid then tore through the Bangladesh batting order, taking 5/55 to send the hosts crashing for 205 as the visitors took a huge 137-run first innings lead.
In their second innings, Bangladesh kept losing wickets at regular intervals.
Liton Das made just nine before he was trapped leg before wicket by Zahir Khan, who then scalped Mosaddek Hossain for 12.
Batting mainstay Mushfiqur Rahim stroked 23 with four boundaries before he fell leg before wicket to Rashid, who dismissed Mominul Haque (3) in the same fashion in his next over.
Opener Shadman Islam batted patiently for his 41 but was trapped leg before wicket by Mohammad Nabi, while Rashid bagged the wicket of Mahmudullah to leave Bangladesh in further strife before rain brought an early finish to proceedings.
