In the end, Rashid Khan, the skipper, and Naveen-ul-Haq each claimed four wickets to lead Afghanistan to a historic victory.
Bangladesh had to win handily in order to qualify on net run-rate (NRR), as they were also aiming to make it to their first World Cup semi-final.
Leg-spinner Rishad Hossain (3-26) dismissed both Rahmanullah Gurbaz and Ibrahim Zadran, the dangerous opening duo from Afghanistan, after they were successfully throttled. However, Rashid blasted three late sixes to increase the score.