Regions of contact between cells are frequently enriched in or depleted of certain protein or lipid species. Here, we explore a possible physical basis that could contribute to this membrane heterogeneity using a model system of a giant vesicle tethered to a planar supported bilayer. Vesicles contain coexisting liquid-ordered (L_o) and liquid-disordered (L_d) phases at low temperatures and are tethered using trace quantities of adhesion molecules that preferentially partition into one liquid phase. We find that the L_d marker DiI-C₁₂ is enriched or depleted in the adhered region when adhesion molecules partition into L_d or L_o phases, respectively. Remarkably, adhesion stabilizes an extended zone enriched or depleted of DiI-C₁₂ even at temperatures >15°C above the miscibility phase transition when membranes have compositions that are in close proximity to a critical point. A stable adhesion zone is also observed in plasma membrane vesicles isolated from living RBL-2H3 cells, and probe partitioning at 37°C is diminished in vesicles isolated from cells with altered cholesterol levels. Probe partitioning is in good quantitative agreement with predictions of the two-dimensional Ising model with a weak applied field for both types of model membranes. These studies experimentally demonstrate that large and stable domain structure can be mediated by lipids in single-phase membranes with supercritical fluctuations.