We study numerically and experimentally the penetration and evaporation dynamics of droplets wicking into a thin double-layered porous material with order-of-magnitude difference in the physical properties between the layers. We show that such double-layered porous materials can be used to create highly asymmetrical wicking properties, preventing liquid droplets wicking from one surface to the other, while allowing wicking in the reverse direction. In addition, these double-layered porous materials are shown to reduce the evaporation time of droplets penetrating into the porous material, compared with a single-layered porous material of equal thickness and physical properties similar to either of the layers.