Over million years, convergence between the Nazca and South America tectonic plates results in Andean orogeny. Over decades/centuries, it fuels the earthquake cycle of the Andean megathrust. It is well recognised that, over the geologically-long term of million years, Andean orogeny feeds back onto plate convergence rates, generating temporal changes documented throughout the Neogene. In contrast, no feedback mechanism operated over the geologically-short term by the earthquake cycle is currently contemplated. In fact, it is commonly assumed that the rates of contemporary convergence, which are accurately measured via geodesy, remain steady during the megathrust earthquake cycle. Here we investigate whether the contemporary Nazca/South America plate motion varies over year-/decade-long periods in response to megathrust stress variations associated with the earthquake cycle. We focus on the decade preceding the three largest and most recent M_w>8 earthquakes (2010 M_w=8.8 Maule, 2014 M_w=8.1 Iquique, 2015 M_w=8.3 Illapel), and find slowdowns of both Nazca and South America whole-plate motions that exceed the impact of data uncertainty or noise. We show that the torque variations required upon Nazca and South America to generate the slowdowns are consistent with that arising from the buildup of interseismic stress preceding the earthquakes.