Manifested from the "tears of wine" to the "coffee-ring effect", the directional transport of a liquid governed by the Marangoni effect is highly pervasive in our daily life and has brought a great number of applications. Similar to this surface tension gradient-dominated process, the fluid preferentially flows from the hot region to the cold region. In contrast to this perception, in this study, we report that water liquid deposited on a specially designed topological surface can flow from the low-temperature region to the high-temperature region in a spontaneous, long-range, and unidirectional manner. We show that such a behavior is mainly owing to a strong topological effect that outweighs the thermal gradient imposed along the surface. Moreover, the specific temperature range applied on the topological surface for the occurrence of such a unidirectional liquid transport phenomenon is also identified. Our findings would find important insights for developing next-generation cooling devices where a rapid flow from the condensation region to the evaporation/boiling region is preferred.