A dispenser for dispensing a substance, such as a liquid lipstick or other product, has a body defining a variable-volume storage chamber for storing the product. A dispensing portion is connected with the body and defines a bore coupled in fluid communication with the storage chamber for receiving product therefrom, and an outlet aperture coupled in fluid communication with the bore. A piston is received within the bore, and a one-way valve is mounted on the dispensing portion for dispensing metered amounts of product therethrough. The one-way valve has an axially-extending valve seat, and an axially-extending 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 piston for moving the piston within the bore and dispensing a predetermined amount of product within the bore through the outlet aperture.