The Afghans took an unassailable 2-0 lead in the three-match series with a 6-wicket win in second match.
They reached the target of 135 with more than one over to spare after Shakib Al Hasan decided to bat first at Rajiv Gandhi International Cricket Stadium on Tuesday.
The 19-year old leg-spinner tore through the Bangladesh battling to restrict them to below-par 134, a total that was at least 20 runs short.
He also claimed the scalp of returning Soumya Sarkar with the penultimate ball of his spell to bag his second straight man-of-the-match award.
Openers Mohammad Shahzad (24) and Usman Ghani (21) were slow to get off the blocks and perished trying to break the shackles after left-arm spinner Nazmul Islam bowled two maidens.
The Bangladesh bowlers managed to stem the run flow and pile pressure on the batsmen with the required run rate creeping up. They needed 46 from the last five overs and it appeared the game may go down to the wire.
But Samiullah Shenwari and Mohammad Nabi held the nerves and then finished the game with some crisp strokeplay.
Promoted up the order, Shenwari launched the attack towards the slog overs before he was dismissed just one run short of what would have been a well-deserved half century.
Nabi then drew on his experience and got his side over the line striking two fours and as many sixes in the 19th over to remain unbeaten 31 off 15, thereby securing Afghanistan’s fourth series victory.
He also shone with the ball claiming the wickets of Sabbir Rahman (9) and Mushfiqur Rahim (22).
Earlier, Abu Hider slogged 21 off 14 to take the Tigers past 130 and give his team something to bowl at.
The Afghan spin troika of Rashid, Mujeeb Ur Rahman and Nabi claimed six wickets for 46 runs in 12 overs to assert their dominance over the Bangladesh batsmen.
The Tigers had lost opener Liton Das and Sabbir early.
Liton pulled Shapoor Zadran in the second over and found Rashid at deep square-leg.
Sabbir (13) hit Zardan the next over for three consecutive fours and then went back trying to take on Nabi as well.
After starting aggressively with a six and a four, Mahmudullah (14 off 8) could not go the distance and was bowled by Karim Janat.
The Tigers had lost the first match by huge 45 runs after batting and bowling failures.
The final match will be played at the same venue on Thursday.