A dispenser for dispensing a substance, such as a liquid lipstick or other cosmetic, pharmaceutical or cosmeceutical product, has a body with a variable-volume storage chamber for storing the product. A dispensing portion is connected with the body and a one-way valve for dispensing amounts of product therethrough. The dispensing portion defines a compression chamber in fluid communication with the storage chamber for receiving product therefrom, and an outlet aperture coupled in fluid communication with the compression chamber. The one-way valve has a valve seat, and a visco-elastic valve cover seated on the valve seat and defining a normally-closed, axially-extending seam therebetween forming a fluid-tight seal between the valve cover and valve seat. The flexible valve cover is movable relative to the valve seat, and the seam is connectable in fluid communication with the outlet aperture to allow the passage of product through the seam and out of the dispenser. An actuator is drivingly connected to the compression chamber for pressurizing product within the compression chamber and dispensing an amount of product within the compression chamber.