We have for the first time achieved cavity ignition and sustainable combustion of liquid kerosene in supersonic flow of Mach number 2.52 using a laser-induced plasma (LIP) on a model supersonic combustor equipped with dual cavities in tandem as flameholders. The liquid kerosene of ambient temperature is injected from the front wall of the upstream cavity, while the ignitions have been conducted in both cavities. High-speed chemiluminescence imaging shows that the flame kernel initiated in the downstream cavity can propagate contraflow into upstream cavity and establish full sustainable combustion. Based on the qualitative distribution of the kerosene vapor in the cavity, obtained using the kerosene planar laser-induced fluorescence technique, we find that the fuel atomization and evaporation, local hydrodynamic and mixing conditions in the vicinity of the ignition position and in the leading edge area of the cavity have combined effects on the flame kernel evolution and the eventual ignition results.