The synthetic pathways of life's building blocks are envisaged to be through a series of complex prebiotic reactions and processes. However, the strategy to compartmentalize and concentrate biopolymers under prebiotic conditions remains elusive. Liquid-liquid phase separation is a mechanism by which membraneless organelles form inside cells, and has been hypothesized as a potential mechanism for prebiotic compartmentalization. Associative phase separation of oppositely charged species has been shown to partition RNA, but the strongly negative charge exhibited by RNA suggests that RNA-polycation interactions could inhibit RNA folding and its functioning inside the coacervates. Here, we present a prebiotically plausible pathway for non-associative phase separation within an evaporating all-aqueous sessile droplet. We quantitatively investigate the kinetic pathway of phase separation triggered by the non-uniform evaporation rate, together with the Marangoni flow-driven hydrodynamics inside the sessile droplet. With the ability to undergo liquid-liquid phase separation, the drying droplets provide a robust mechanism for formation of prebiotic membraneless compartments, as demonstrated by localization and storage of nucleic acids, in vitro transcription, as well as a three-fold enhancement of ribozyme activity. The compartmentalization mechanism illustrated in this model system is feasible on wet organophilic silica-rich surfaces during early molecular evolution.