We report a new phenomenon, resonant separatrix activation (RSA), in which a significant decrease in an activation barrier occurs due to weak periodic driving at the appropriate frequency. This decrease greatly exceeds the maximum decrease caused by adiabatic driving of the same amplitude. RSA is observed in weakly-dissipative systems possessing two or more saddles. The mechanism is a strong resonant quasi-regular variation of energy within the area of transient chaos related to the saddle-associated separatrix(ces) of the undriven system. The most pronounced RSA occurs when the saddles have different energies, and this difference ΔE is comparable to the original activation barrier: the resonant driving provides inter-separatrix transport, thus reducing the activation barrier by ΔE. RSA can be observed in natural systems, e.g. in fluidic, atmospheric and planetary transport, and can be used in engineered systems with a large quality factors, e.g. NEMS/MEMS.