The Leidenfrost effect is a technically and industrially important phenomenon that severely restricts heat removal from high-heat-flux surfaces. A simple remedy to the Leidenfrost effect is provided by polymer nanofiber mats created and deposited by electrospinning on stainless steel surfaces. The influence of nanofiber mats on hydrodynamics and cooling efficiency of single drop impact onto hot surfaces has been investigated experimentally. The evolution of the drops has been recorded by a high-speed complimentary metal-oxide semiconductor camera, whereas the cooling temperature was measured by a thermocouple. A remarkable phenomenon was discovered: a mat of polymer nanofibers electrospun onto a heater surface can completely suppress the Leidenfrost effect, thereby increasing the rate of heat removal from the surface to the liquid drops significantly. The "inverse-Leidenfrost" effect is described qualitatively and quantitatively, providing clear physical reasons for the observed behavior.