Since flat subduction of the Nazca Plate beneath Peru was first recognized in the 1970s and 1980s a satisfactory explanation has eluded researchers. We present evidence that a lost oceanic plateau (Inca Plateau) has subducted beneath northern Peru and propose that the combined buoyancy of Inca Plateau and Nazca Ridge in southern Peru supports a 1500 km long segment of the downgoing slab and shuts off arc volcanism. This conclusion is based on an analysis of the seismicity of the subducting Nazca Plate, the structure and geochemistry of the Marquesas Plateau as well as tectonic reconstructions of the Pacific-Farallon spreading center 34 to 43 Ma. These restore three sub-parallel Pacific oceanic plateaus; the Austral, Tuamotu and Marquesas, to two Farallon Plate counterparts; the Iquique and Nazca Ridges. Inca Plateau is apparently the sixth and missing piece in an ensemble of 'V-shaped' hotspot tracks formed at on-axis positions. We argue the mirror image of the Inca Plateau, the Marquesas Plateau, is an ancient edifice overprinted by recent volcanism, in disagreement with the widely accepted young (<5 Ma) hotspot model for plateau formation.