We report here the observation of a new self-oscillation mechanism in nanoelectromechanical systems (NEMS). A highly resistive nanowire was positioned to form a point-contact at a chosen vibration node of a silicon carbide nanowire resonator. Spontaneous and robust mechanical oscillations arise when a sufficient DC voltage is applied between the two nanowires. An original model predicting the threshold voltage is used to estimate the piezoresistivity of the point-contact in agreement with the observations. The measured input power is in the pW-range which is the lowest reported value for such systems. The simplicity of the contacting procedure and the low power consumption open a new route for integrable and low-loss self-excited NEMS devices.