Published slip distribution models, based on geodetic, seismological and tsunami data, of the M-w 7.8, 2010 Mentawai tsunami earthquake offshore south-central Sumatra, suggest that the large tsunami wave was generated by a narrow swath of high seafloor uplift along the accretionary wedge front, implying higher vertical throw than that consistent with slip on the shallow-dipping megathrust. Here we present high-resolution seismic reflection profiles across the 2010 rupture zone that image the youngest deformation at the accretionary wedge front. The profiles reveal conjugate, steeply-dipping, active thrust faults that branch upwards from the megathrust and bound triangular pop-ups. The seismologically determined co-seismic slip (>= 10 m) on the 6 degrees-dipping decollement probably caused a comparable amount of upward expulsion of these similar to 3 km-wide, flat-topped pop-ups. Co-seismic throw on the approximate to 60 degrees dipping thrusts that bound the pop-up plateaus maximize the uplift of the seafloor and overlying water-column, providing an additional localised tsunami source. Tsunami simulations show that such combined deformation, i.e. the broad-scale seafloor displacement caused by slip on the megathrust and the localized 8-10 m seafloor uplift across a 6-9 km-wide pop-up belt involving up to three pop-ups, is able to reproduce the 2010 tsunami amplitude measured by a DART buoy, and observed run-up heights in the Mentawai Islands. This simple mechanism, observed in analogue sandbox shortening experiments, may thus efficiently generate the oversize waves that characterize Tsunami-Earthquakes. Systematic mapping of pop-ups along accretionary wedge fronts may help identify trench segments prone to produce the special class of seismic events that spawn exceptionally large tsunamis.