In the present work, we described the activity of the thiosemicarbazone derived from 5,6-dimethoxy-1-indanone (TSC), which we previously characterized as a new compound that inhibits bovine viral diarrhea virus (BVDV) infection. We showed that TSC acts at a point of time that coincides with the onset of viral RNA synthesis and that it inhibits the activity of BVDV replication complexes (RCs). Moreover, we have selected five BVDV mutants that turned out to be highly resistant to TSC but still susceptible to ribavirin (RBV). Four of these resistant mutants carried an N264D mutation in the viral RNA-dependent RNA polymerase (RdRp). The remaining mutant showed an A392E mutation within the same protein. Some of these mutants replicated slower than the wild-type (wt) virus in the absence of TSC, whereas others showed a partial reversion to the wt phenotype over several passages in the absence of the compound. The docking of TSC in the crystal structure of the BVDV RdRp revealed a close contact between the indane ring of the compound and several residues within the fingers domain of the enzyme, some hydrophobic contacts, and hydrogen bonds with the thiosemicarbazone group. Finally, in the mutated RdRp from resistant BVDV, these interactions with TSC could not be achieved. Interestingly, TSC inhibited BVDV replication in cell culture synergistically with RBV. In conclusion, TSC emerges as a new nonnucleoside inhibitor of BVDV RdRp that is synergistic with RBV, a feature that turns it into a potential compound to be evaluated against hepatitis C virus (HCV).