The Mw 7.5 earthquake that struck Central Sulawesi, Indonesia, on September 28, 2018, was rapidly followed by coastal landslides and destructive tsunami waves within Palu Bay. Here, we present new tsunami modeling that supports a dual source mechanism from the supershear strike-slip earthquake and coastal landslides. Up until now the tsunami mechanism: earthquake, coastal landslides, or a combination of both, has remained controversial, because published research has been inconclusive; with some studies explaining most observations from the earthquake and others the landslides. Major challenges are the numerous different earthquake source models used in tsunami modeling, and that landslide mechanisms have been hypothetical. Here, we simulate tsunami generation using three published earthquake models, alone and in combination with seven coastal landslides identified in earlier work and confirmed by field and bathymetric evidence which, from video evidence, produced significant waves. To generate and propagate the tsunamis, we use a combination of two wave models, the 3D non-hydrostatic model NHWAVE and the 2D Boussinesq model FUNWAVE-TVD. Both models are nonlinear and address the physics of wave frequency dispersion critical in modeling tsunamis from landslides, which here, in NHWAVE are modeled as granular material. Our combined, earthquake and coastal landslide, simulations recreate all observed tsunami runups, except those in the southeast of Palu Bay where they were most elevated (10.5 m), as well as observations made in video recordings and at the Pantoloan Port tide gauge located within Palu Bay. With regard to the timing of tsunami impact on the coast, results from the dual landslide/earthquake sources, particularly those using the supershear earthquake models are in good agreement with reconstructed time series at most locations. Our new work shows that an additional tsunami mechanism is also necessary to explain the elevated tsunami observations in the southeast of Palu Bay. Using partial information from bathymetric surveys in this area we show that an additional, submarine landslide here, when simulated with the other coastal slides, and the supershear earthquake mechanism better explains the observations. This supports the need for future marine geology work in this area.