The Colorado Plateau of the southwestern United States is characterized by a bowl-shaped high elevation, late Neogene–Quaternary magmatism at its edge, large gradients in seismic wave velocity across its margins, and relatively low lithospheric seismic wave velocities. We explain these observations by edge-driven convection following rehydration of Colorado Plateau lithosphere. A rapidly emplaced Cenozoic step in lithosphere thickness between the Colorado Plateau and adjacent extended Rio Grande rift and Basin and Range province causes small-scale convection in the asthenosphere. A lithospheric drip below the plateau is removing lithosphere material from the edge that is heated and metasomatized, resulting in magmatism. Edge-driven convection also drives margin uplift, giving the plateau its characteristic bowl shape. The edge-driven convection model shows good consistency with features resolved by seismic tomography.