We demonstrate complete all-optical and phase-stable control of the linear optical polarization and the nonlinear coherent response (third-harmonic generation) of a hybrid nanoplasmonic-photonic system. A few tens of femtoseconds after the excitation, we turn the response on and off at any given point in time and probe its temporal evolution throughout the control process with a three-pulse nonlinear optical technique. After being switched off, the polarization and the nonlinear radiation remain off permanently. All experiments agree well with numerical simulations based on a damped harmonic oscillator model.