We study the shift in the critical temperature T-c in binary mixtures in strong electric fields. In experiments we measure the nonlinear dielectric effect (NDE) in a mixture of nitrobenze and n-octane and calculate Piekara's factor. We find that the critical anomaly of Piekara's factor is a function of an electric field strength. We propose to explain this observation as a result of a downward shift of T-c, and this allows us to calculate (partial derivative T-c/partial derivative E-2) = (-22 +/- 10) X 10(-16) (K m(2))/V-2. In the theoretical part we amend Landau and Lifshitz's formula and show that the downward shift of T-c can be estimated from a simple mean-field theory taking into account the linear and quadratic terms in an expansion of the constitutive relation epsilon(x) between the electric constant epsilon and mixture composition x.