A drainless reverse osmosis (RO) water purification system provides relatively pure water for on-demand dispensing, while recycling brine to a domestic hot water system. The drainless purification system includes a pre-filter catalyst cartridge for removing chlorine-based contaminants from a tap water supply upstream from an RO membrane. The catalyst is regularly refreshed by a high through-flow of water to a conventional cold water dispense faucet, thereby significantly prolonging the service life of the RO membrane. The RO membrane is incorporated into a multi-cartridge unit adapted for facilitated slide-out removal and replacement as needed. A control valve recycles brine from the RO membrane to the hot water system during pure water production, and recirculates tap water through the RO membrane when a pure water reservoir is substantially filled. The multi-cartridge unit may further include an air filtration system for providing a flow of filtered air.