A search for pair production of the supersymmetric partner of the top quark, the top squark, in proton-proton collisions at s = 13 TeV is presented in final states containing at least one hadronically decaying tau lepton and large missing transverse momentum. This final state is highly sensitive to scenarios of supersymmetry in which the decay of the top squark to tau leptons is enhanced. The search uses a data sample corresponding to an integrated luminosity of 138 fb⁻¹, which was recorded with the CMS detector during 2016–2018. No significant excess is observed with respect to the standard model predictions. Exclusion limits at 95% confidence level on the masses of the top squark and the lightest neutralino are presented under the assumptions of simplified models. The results probe top squark masses up to 1150 GeV for a nearly massless neutralino. This search covers a relatively less explored parameter space in the context of supersymmetry, and the exclusion limit is the most stringent to date for the model considered here.