Liquid-liquid phase separation (LLPS) is a mechanism by which membraneless organelles form inside cells, and has been hypothesized as a mechanism for prebiotic compartmentalization. Here we present a prebiotically plausible pathway for non-associative phase separation, which could drive biopolymer self-organization and compartmentalization to form the earliest membraneless compartments, within an evaporating all-aqueous sessile droplet. Through a quantitative understanding of the kinetic pathway of phase separation, we find that non-uniform evaporation rates across the droplet surface induce compositional gradients and surface tension differences, triggering LLPS and polymer self-organization inside the sessile droplet. With the ability to undergo LLPS, the drying droplets provide a robust mechanism for formation of prebiotic membraneless compartments. These self-organized membraneless compartments, with volumes comparable to subcellular structures, could represent a mechanism for the enrichment of information-carrying molecules and formation of RNA-containing organelles. We demonstrated compartmentalized localization and storage of nucleic acids, in vitro transcription, as well as a three-fold enhancement of ribozyme activity. This model system demonstrates a cell-like, aqueous, macromolecular crowded and thermodynamically non-equilibrium microenvironment. Such a mechanism for compartmentalization is feasible on wet organophilic silica-rich surfaces during early molecular evolution.