While most oceanic volcanism is associated with the passive rise of hot mantle beneath the spreading axes of mid-ocean ridges (MOR), volcanism occurring off-axis reflects intraplate upper-mantle dynamics and composition, yet is poorly understood. Off the south East Pacific Rise (SEPR), volcanism along the Pukapuka, Hotu-Matua, and Sojourn ridges has been attributed to various mechanisms, but none can reconcile its spatial, temporal, and geochemical characteristics. Our three-dimensional numerical models show that asthenospheric shear can excite upwelling and decompression melting at the tip of low-viscosity fingers that are propelled eastward by vigorous sublithospheric flow. This shear-driven upwelling is able to sustain intraplate volcanism that progresses toward the MOR, spreads laterally close to the axis, and weakly continues on the opposite plate. These predictions can explain the anomalously fast eastward progression of volcanism, and its spatial distribution near the SEPR. Moreover, for a heterogeneous mantle source involving a fertile component, the predicted systematics of volcanism can explain the geochemical trend along Pukapuka and the enriched anomaly of SEPR mid-oceanic ridge basalt at 16°–20.5°S. Our study highlights the role of horizontal asthenospheric flow and mantle heterogeneity in producing linear chains of intraplate volcanism independent of a (deep-rooted) buoyancy source.