The Tykes fell behind to a Steven Fletcher strike but hit back 60 seconds later through Jon Macken and then in first-half stoppage time with a spectacular strike from AndersonDeSilva.
The left-handed Tamim produced some exquisite pull shots, showed complete disregard for England's cricketer of the year Graeme Swann, and blazed one drive through the covers off Anderson that was reminiscent of Aravinda deSilva.