Although volcanism in the southwestern United States has been studied extensively, its origin remains controversial. Various mechanisms such as mantle plumes, upwelling in response to slab sinking, and small-scale convective processes have been proposed, but have not been evaluated within the context of rapidly shearing asthenosphere that is thought to underlie this region. Using geodynamic models that include this shear, we here explore spatiotemporal patterns of mantle melting and volcanism near the Colorado Plateau. We show that the presence of viscosity heterogeneity within an environment of asthenospheric shearing can give rise to decompression melting along the margins of the Colorado Plateau. Our models indicate that eastward shear flow can advect pockets of anomalously low viscosity toward the edges of thickened lithosphere beneath the plateau, where they can induce decompression melting in two ways. First, the arrival of the pockets critically changes the effective viscosity near the plateau to trigger smallscale edge-driven convection. Second, they can excite shear-driven upwelling (SDU), in which horizontal shear flow becomes redirected upward as it is focused within the low-viscosity pocket. We find that a combination of ''triggered'' edge-driven convection and SDU can explain volcanism along the margins of the Colorado Plateau, its encroachment toward the plateau's southwestern edge, and the association of volcanism with slow seismic anomalies in the asthenosphere. Geographic patterns of intraplate volcanism in regions of vigorous asthenospheric shearing may thus directly mirror viscosity heterogeneity of the sublithospheric mantle.