A linerless closure for use on an associated container includes a unitary, one-piece closure body having a top wall portion, and an annular skirt portion depending from the top wall portion. The closure includes an annular, outer seal element which depends from the top wall portion for sealing engagement with a generally outwardly facing surface of the associated container. The closure includes an inner, plug seal element depending from the top wall portion for sealing engagement with a generally inwardly facing surface of the container. Notably, the closure includes a discontinuous pressure block in the form of a plurality of circumferentially spaced, seal reinforcement elements on the inside surface of the skirt portion, adjacent the top wall portion. The reinforcement elements are engageable by the outer seal element to limit outward deflection of the outer seal element, to enhance sealing cooperation with the associated container.