A cosmetic dispenser, includes an applicator having an applicator portion and a cap portion, the cap portion having an inwardly facing screw thread; a container member having a body portion defining a product reservoir and having a neck portion extending from the body portion to receive the applicator, the neck portion having an outwardly facing screw thread for threadedly engaging the inwardly facing screw thread; and a smooth-walled thread guide portion extending from one screw thread of the inwardly facing screw thread and the outwardly facing screw thread toward an opposing screw thread of the inwardly facing screw thread and the outwardly facing screw thread, the thread guide portion being sized to slidingly engage the opposing screw thread so as to guide the opposing screw thread to the one screw thread in proper alignment for threaded engagement.