A range of several fault segments often sequentially ruptures during an earthquake. We investigated the effects of thermal pressurization on dynamic rupture propagation beyond fault discontinuities by simulating spontaneous rupture propagation on two vertical strike-slip fault segments. We revealed that a rupture can jump wider stepovers owing to thermal pressurization and that thermal pressurization on a primary (nucleating) fault enables a rupture to jump at deep portions. In previous numerical studies on dry fault systems, it was found that a rupture sometimes fails to propagate to an unconnected fault, which is observed in the case of real earthquakes, and a rupture that successfully propagates is usually triggered near the Earth's surface, unlike rupture evolution images obtained by seismic waveform modeling. Thermal pressurization can explain the inconsistencies between the previous numerical simulations and the observations, without depending on the heterogeneity of the initial stress and/or friction. Under depth-dependent stress, we showed that thermal pressurization enables a rupture to jump much wider stepovers at deep portions. If thermal pressurization is in effect on faults, hydraulic diffusivity along with fault geometry can strongly control the characteristics of rupture propagation at fault discontinuities.