Blind source separation involves the estimation of mixing matrix given only observed mixtures. Considering the computational cost in practice, this paper proposes an efficient mixing matrix estimation (MME) method using an easily configured two-sensor array. Time-frequency (TF) analysis, which has been an important field of research for MME, is invoked herein to precisely detect single-source TF points (SSPs) in combination with the principle of matching pursuit. We theoretically verify that the residual TF vectors at SSPs derived by mixture TF vectors tend to have zero-valued elements, based on which a criterion is designed to identify a set of exact SSPs for accurate MME. Furthermore, the number of sources can be simultaneously estimated by adopting mean-shift clustering on SSPs. Numerical simulations are carried out on both real-valued and complex-valued mixing matrices to provide corroborating evidence for the theoretical claims.