It is shown that the two-center bridged tunneling contact in the serial configuration based on the donor–acceptor single redox molecule immersed in the electrolyte solution at the ambient conditions (i.e., room temperature and condensed matter environment) demonstrates pronounced transistor-like features for certain sets of the physical parameters of the system. Electrons at the redox centers of the bridge molecule are coupled strongly to the classical phonon modes of the condensed matter environment and Debye screening of the electric field is taken into account. The case of the non-adiabatic tunneling of electrons between the centers and between the centers and electrodes is considered and the limit of the infinite Coulomb repulsion between electrons occupying the same center is used. The regions of the physical parameters where both strong rectification and strong amplification (over three orders of magnitude) take place for all positive (or negative) values of the bias voltage are revealed and the transistor-like current/bias voltage characteristics are calculated.