Results are presented from a search for the pair production of third-generation scalar and vector leptoquarks, as well as for top squarks in R-parity-violating supersymmetric models. In either scenario, the new, heavy particle decays into a τ lepton and a b quark. The search is based on a data sample of pp collisions at sqrt[s] = 7 TeV, which is collected by the CMS detector at the LHC and corresponds to an integrated luminosity of 4.8 fb(-1). The number of observed events is found to be in agreement with the standard model prediction, and exclusion limits on mass parameters are obtained at the 95% confidence level. Vector leptoquarks with masses below 760 GeV are excluded and, if the branching fraction of the scalar leptoquark decay to a τ lepton and a b quark is assumed to be unity, third-generation scalar leptoquarks with masses below 525 GeV are ruled out. Top squarks with masses below 453 GeV are excluded for a typical benchmark scenario, and limits on the coupling between the top squark, τ lepton, and b quark, λ(333)(') are obtained. These results are the most stringent for these scenarios to date.