On ocean basaltic volcanoes, magma transfer to the surface occurs along sub-vertical ascent from the mantle lithosphere through the oceanic crust and the volcanic edifice, eventually followed by lateral propagation along rift zones. We use a 17-years-long database of volcano-tectonic seismic events and a detailed mapping of the pyroclastic cones to determine the geometry and the dynamics of the magma paths intersecting the edifice of Piton de la Fournaise volcano. We show that the overall plumbing system, from about 30 km depth to the surface, is composed of two structural levels that feed distinct types of rift zones.