Liquid water at ambient temperature displays ultrafast molecular motions and concomitant fluctuations of very strong electric fields originating from the dipolar H2O molecules. We show that such random intermolecular fields induce the tunnel ionization of water molecules, which becomes irreversible if an external terahertz (THz) pulse imposes an additional directed electric field on the liquid. Time-resolved nonlinear THz spectroscopy maps charge separation, transport, and localization of the released electrons on a few-picosecond time scale. The highly polarizable localized electrons modify the THz absorption spectrum and refractive index of water, a manifestation of a highly nonlinear response. Our results demonstrate how the interplay of local electric field fluctuations and external electric fields allows for steering charge dynamics and dielectric properties in aqueous systems.