A connector for use with a disposable flexible liner installed in a basin to contact liquid is provided to bridge between an overflow opening provided in the liner and an overflow aperture provided in an upright wall of the basin, so that when liquid containable in an interior volume of the basin exceeds a prescribed height, the liquid is enabled to drain out of the interior volume through the liner at the communicated openings/apertures. A conduit formed by the connector for insertion into the basin to bridge between the communicated openings/apertures is arranged for a friction fit in an overflow throat extending from the overflow aperture defined in the basin. A related method for using a replaceable liner in a basin having an overflow aperture is also disclosed.