The devastating tsunami after the 2018 Indonesian Sulawesi-Palu strike-slip earthquake was a surprise because strike-slip faulting is a known phenomenon of primarily lateral movement of land, while tsunamis are believed to be caused by vertical movement of seafloor. Here we show that the horizontal displacement of seafloor slopes, instead of the vertical movement or land-sliding, was the primary cause of the tsunami. We reconstructed the earthquake from seismographs and satellite data, and used the earthquake-induced momentum to replicate the tsunami. We found that the strike-slip faulting could generate multiple tsunami sources by pushing waters laterally. Sources from the deeper slopes caused the deadly long-wave tsunami hit the Palu city, while sources outside the Palu bay resulted in the “early arrival” tsunami at Mamuju, explained observations that could not be reconciled previously. Our findings suggest a new approach of using lateral movement of faulting to detect tsunamis for early warning.