The importance of a low-viscosity asthenosphere underlying mobile plates has been highlighted since the earliest days of the plate tectonics revolution. However, absolute asthenospheric viscosities are still poorly constrained, with estimates spanning up to 3 orders of magnitude. Here we follow a new approach using analytic solutions for Poiseuille-Couette channel flow to compute asthenospheric viscosities under the Caribbean. We estimate Caribbean dynamic topography and the associated pressure gradient, which, combined with flow velocities estimated from geologic markers and tomographic structure, yield our best-estimate asthenospheric viscosity of (3.0 ± 1.5)*1018 Pa s. This value is consistent with independent estimates for non-cratonic and oceanic regions, and challenges the hypothesis that higher-viscosity asthenosphere inferred from postglacial rebound is globally-representative. The active flow driven by Galapagos plume overpressure shown here contradicts the traditional view that the asthenosphere is only a passive lubricating layer for Earth's tectonic plates.