The present invention is directed to a bag-in-box package having a flowable product contained in a thermoplastic bag which is inserted in or encased within an outer relatively rigid box or carton is provided. The box or carton may be constructed from a rigid or semi-rigid plastic or paperboard and has (i) a flat bottom panel, an opposing top panel, and a self-supporting, upstanding wall connecting the bottom and top panels, and (ii) an access port through the box for inserting a rigid implement, such as a drinking straw or other spout/tap therethrough to puncture the bag and withdraw the flowable product from inside the bag. The flowable product occupies less than 100% of the available volume of the bag and the remaining available head-space volume above the product is evacuated or collapsed in order to prevent spillage or leakage of product from the straw or spout when the bag is punctured.
