Membrane technologies that enable the efficient purification of impaired water sources are needed to address growing water scarcity. However, state-of-the-art engineered membranes are constrained by a universal, deleterious trade-off where membranes with high water permeability lack selectivity. Current membranes also poorly remove low-molecular weight neutral solutes and are vulnerable to degradation from oxidants used in water treatment. We report a water desalination technology that uses applied pressure to drive vapor transport through membranes with an entrapped air layer. Since separation occurs due to a gas-liquid phase change, near-complete rejection of dissolved solutes including sodium chloride, boron, urea, and N-nitrosodimethylamine is observed. Membranes fabricated with sub-200-nm-thick air layers showed water permeabilities that exceed those of commercial membranes without sacrificing salt rejection. We also find the air-trapping membranes tolerate exposure to chlorine and ozone oxidants. The results advance our understanding of evaporation behavior and facilitate high-throughput ultraselective separations.