The resonant substructure of B-s(0) -> (D) over bar K-0(-)pi(+) decays is studied using a data sample corresponding to an integrated luminosity of 3.0 fb(-1) of pp collision data recorded by the LHCb detector. An excess at m((D) over bar K-0(-)) approximate to 2.86 GeV/c(2) is found to be an admixture of spin-1 and spin-3 resonances. Therefore, the D-sJ*(2860)(-) state previously observed in inclusive e(+)e(-) -> (D) over bar (K-X)-K-0 and pp -> (D) over bar (K-X)-K-0 processes consists of at least two particles. This is the first observation of a heavy flavored spin-3 resonance, and the first time that any spin-3 particle has been seen to be produced in B decays. The masses and widths of the new states and of the D-s2*(2573)(-) meson are measured, giving the most precise determinations to date.