Molecular doping and detection are at the forefront of graphene research, a topic of great interest in physical and materials science. Molecules adsorb strongly on graphene, leading to a change in electrical conductivity at room temperature. However, a common impediment for practical applications reported by all studies to date is the excessively slow rate of desorption of important reactive gases such as ammonia and nitrogen dioxide. Annealing at high temperatures, or exposure to strong ultraviolet light under vacuum, is employed to facilitate desorption of these gases. In this article, the molecules adsorbed on graphene nanoflakes and on chemically derived graphene-nanomesh flakes are displaced rapidly at room temperature in air by the use of gaseous polar molecules such as water and ethanol. The mechanism for desorption is proposed to arise from the electrostatic forces exerted by the polar molecules, which decouples the overlap between substrate defect states, molecule states, and graphene states near the Fermi level. Using chemiresistors prepared from water-based dispersions of single-layer graphene on mesoporous alumina membranes, the study further shows that the edges of the graphene flakes (showing p-type responses to NO2 and NH3) and the edges of graphene nanomesh structures (showing n-type responses to NO2 and NH3) have enhanced sensitivity. The measured responses towards gases are comparable to or better than those which have been obtained using devices that are more sophisticated. The higher sensitivity and rapid regeneration of the sensor at room temperature provides a clear advancement towards practical molecule detection using graphene-based materials.