Nihaduzzaman then raised hopes of a comeback in Chattogram by removing Tamim and Joy in successive overs.
But Yasir then played a captain’s innings, hitting four sixes and two fours to take Khulna to the finishing line with four balls to spare.
Pakistan’s Azam Khan remained unbeaten on 15 off 16 balls at the other end.
This is Khulna’s second consecutive win after three consecutive losses in the tournament.
Khulna has now moved up to the fourth position with four points while the losers, Chattogram, have slipped to the sixth position.