The Andean cordillera was constructed during compressive tectonic events, whose causes and controls remain unclear. Exploring a possible link to plate convergence has been impeded by the coarse temporal resolution of existing plate kinematic models. Here we show that the Neogene evolution of the Andean margin is primarily related to changes in convergence as observed in new high-resolution plate reconstructions. Building on a compilation of plate finite rotations spanning the last 30 million years and using noise-mitigation techniques, we predict several short-term convergence changes that were unresolved in previous models. These changes are related to main tectono-magmatic events and require forces that are compatible with a range of geodynamic processes. These results allow to revise models of ongoing subduction orogeny at its type locality, emphasizing the role of upper plate deformation in the balance between kinematic energy associated with plate motion and gravitational potential energy stored in orogenic crustal roots.