In cases of both Abelian and non-Abelian gauge groups, we study the Higgs mechanism in the topologically massive gauge theories in an arbitrary space–time dimension. We show that when the conventional Higgs potential coexists with a topological term, gauge fields become massive by "eating" simultaneously both the Nambu–Goldstone boson and a higher-rank tensor field and instead a new massless scalar field is "vomitted" in the physical spectrum. Because of the appearance of this new massless field, the number of the physical degrees of freedom remains unchanged before and after the spontaneous symmetry breakdown. Moreover, the fact that the new field is a physical and positive norm state is rigorously proved by performing the manifestly covariant quantization of the model in three and four dimensions. In the mechanism at hand, the presence of a topological term makes it possible to shift the mass of gauge fields in a nontrivial manner compared to the conventional value.