The efficient transfer of energy between organic and inorganic semiconductors is a widely sought after property, but has so far been limited to the transfer of spin-singlet excitons. Here we report efficient resonant-energy transfer of molecular spin-triplet excitons from organic semiconductors to inorganic semiconductors. We use ultrafast optical absorption spectroscopy to track the dynamics of triplets, generated in pentacene through singlet exciton fission, at the interface with lead selenide (PbSe) nanocrystals. We show that triplets transfer to PbSe rapidly (<1 ps) and efficiently, with 1.9 triplets transferred for every photon absorbed in pentacene, but only when the bandgap of the nanocrystals is close to resonance (±0.2 eV) with the triplet energy. Following triplet transfer, the excitation can undergo either charge separation, allowing photovoltaic operation, or radiative recombination in the nanocrystal, enabling luminescent harvesting of triplet exciton energy in light-emitting structures.