The first observation of the $Omega_b^-toXi_c^+ K^- pi^-$ decay is reported using proton-proton collision data at centre-of-mass energies of $7$, $8$ and $13,mathrm{TeV}$ collected by the LHCb experiment, corresponding to an integrated luminosity of $9,mathrm{fb}^{-1}$. Four excited $Omega_c^0$ baryons are observed in the $Xi_c^+ K^-$ mass projection of the $Omega_b^-toXi_c^+ K^- pi^-$ decays with significance exceeding five standard deviations. Their relative production rates, masses and natural widths are measured, and a test of spin hypotheses is performed. Moreover, the branching ratio of $Omega_b^-toXi_c^+ K^- pi^-$ is measured relative to the $Omega_b^-to Omega_c^0 pi^-$ decay mode and a precise measurement of the $Omega_b^-$ mass of $6044.3 pm 1.2 pm 1.1^{,+0.19}_{,-0.22},mathrm{MeV}$ is obtained.