Directional transport of droplets is crucial for industrial applications and chemical engineering processes, with significant potential demonstrated in water harvesting, microfluidics, and heat transfer. In this work, we present a novel approach to induce self-driving behavior in nanodroplets within a two-dimensional (2D) nanochannel using a strain gradient, as demonstrated through molecular dynamics simulations. Our findings reveal that a small strain gradient imposed along a nanochannel constructed by parallel surfaces can induce water transport at ultrafast velocities (O(102 m s-1)), far exceeding macroscale predictions. Certainly, a larger strain gradient further enhances droplet transport velocity. Additionally, combining a strain gradient with nonparallel surfaces results in up to a 150% increase in transport efficiency. Furthermore, we show that this spontaneous transport mechanism is applicable to nanochannels composed of various 2D materials and successfully establish a reliable theoretical model. These simulation results provide new insights into the directional transport of nanodroplets in 2D nanochannels, opening avenues for advanced applications in nanotechnology and fluid dynamics.