We demonstrate nuclear spin pumping in a single InGaAs/GaAs dot embedded in a p-i-n diode in the regime of resonant optical excitation of spin-polarized electron-hole pairs in the lowest energy states of the dot. A nuclear spin pumping mechanism is proposed relevant to the regime of high electric field where carriers escape from the dot by tunneling. The degree of nuclear spin polarization is shown to increase strongly with the applied electric field, controlling the carrier tunneling from the dot, since at low electric fields the dot is blocked for re-excitation due to the slow hole escape.