Nabi struck an unbeaten 84 off 54 balls to guide Afghanistan to 164-6 before Mujeeb scalped career best 4-15 to help his side bowl out Bangladesh for 139 in 19.5 overs for their world record 12 successive Twenty20 international win.
Mujeeb took three wickets in his opening spell to reduce the home side to 32 for four before Mahmudullah and Sabbir Rahman put a little resistance with 58 runs for the fifth wicket.
Gulbadin Naib broke the partnership by removing Mahmudullah, who made 44 off 39 balls for Bangladesh before Mujeeb ended Sabbir’s innings at 24 in his final over to surpass his previous best of 3-17 against Ireland.