The phenomenon of neutrino flavor oscillations motivates searches for sterile neutrinos in a broad range of masses and mixing-parameter values. A sterile neutrino N that mixes predominantly with the τ neutrino is particularly challenging experimentally. To address this challenge, we propose a new method to search for a ντ-mixing N that is lighter than the τ lepton. The method uses the large e+e-→τ+τ- samples collected at B-factory experiments to produce the N in τ-lepton decays. We exploit the long lifetime of a sterile neutrino in this mass range to suppress background and apply kinematic and vertexing constraints that enable measuring the sterile-neutrino mass. Estimates for the sensitivities of the BABAR, Belle, and Belle II experiments are calculated and presented.