A search is performed for third-generation scalar leptoquarks and heavy right-handed neutrinos in events containing one electron or muon, one hadronically decaying tau lepton, and at least two jets, using a $\sqrt{s}$=13 TeV pp collision data sample corresponding to an integrated luminosity of 12.9 inverse femtobarns collected with the CMS detector at the LHC in 2016. The number of observed events is found to be in agreement with the standard model prediction. A limit is set at 95% confidence level on the product of the leptoquark pair production cross section and beta squared where beta is the branching fraction of leptoquark decay to a tau lepton and a bottom quark. Assuming beta=1, third-generation leptoquarks with masses below 850 GeV are excluded at 95 % confidence level. An additional search based on the same event topology involves heavy right-handed neutrinos, N[R], and right-handed W bosons, W[R], arising in a left-right symmetric extension of the standard model. In this search, W[R] bosons are assumed to decay to a tau lepton and N[R] followed by the decay of the N[R] to a tau lepton and an off-shell W[R] boson. Assuming the mass of the right-handed neutrino to be half of the mass of the right-handed W boson, W[R] boson masses below 2.9 TeV are excluded at 95 % confidence level. These results improve on the limits from previous searches for third-generation leptoquarks and heavy right-handed neutrinos with tau leptons in the final state.