Phosphorylation reactions, driven by competing kinases and phosphatases, are central elements of cellular signal transduction. We reconstituted a native eukaryotic lipid kinase-phosphatase reaction that drives the interconversion of phosphatidylinositol-4-phosphate [PI(4)P] and phosphatidylinositol-4,5-phosphate [PI(4,5)P2] on membrane surfaces. This system exhibited bistability and formed spatial composition patterns on supported membranes. In smaller confined regions of membrane, rapid diffusion ensures the system remains spatially homogeneous, but the final outcome-a predominantly PI(4)P or PI(4,5)P2 membrane composition-was governed by the size of the reaction environment. In larger confined regions, interplay between the reactions, diffusion, and confinement created a variety of differentially patterned states, including polarization. Experiments and kinetic modeling reveal how these geometric confinement effects arise from a mechanism based on stochastic fluctuations in the copy number of membrane-bound kinases and phosphatases. The underlying requirements for such behavior are unexpectedly simple and likely to occur in natural biological signaling systems.