Constraints on couplings of several beyond-Standard-Model-physics scenarios, mediated by massive intermediate particles including ( 1) an extra Z-prime, ( 2) a new light spin-1 boson, and ( 3) a charged Higgs boson, are placed via the neutrino-electron scattering channel to test the Standard Model at a low energy-momentum transfer regime. Data on (nu) over bar (e) - e and nu(e) - e scattering from the TEXONO and LSND, respectively, are used. Upper bounds to coupling constants of the flavor-conserving and flavor-violating new light spin-1 boson and the charged Higgs boson with respect to different mediator masses are determined. The relevant parameter spaces are extended by allowing light mediators. New lower mass limits for extra Z-prime gauge boson models are also placed.