The movement of evaporating liquid droplets on a surface can be triggered by the Marangoni effect arising from heterogeneities in the surface tension or a gradient in the surface energy of the substrate. Here, we show that, on a high energy surface that remains uniform, the motion of two pure liquid droplets can be induced by a gradient in the liquid vapor resulting from evaporation. The droplets always attract each other, moving from the high evaporation side to the low evaporation side, to reduce energy dissipation. By varying the volume of the droplets or the distance between droplets, the motion of the droplets can be effectively controlled.