Resonance low-energy (0-14 eV) electron attachment to natural polyphenolic stilbenes possessing antioxidant properties, namely resveratrol and piceatannol, was investigated by means of dissociative electron attachment spectroscopy. Experimental findings were assigned on base of density functional theory (DFT) calculations of energies and symmetry of vacant molecular orbitals. It was found that characteristic decay of the molecular negative ions of compounds under investigation under gas-phase conditions can be associated with elimination of neutral H₂ molecule and formation of quinone-like structure bearing excess electron. These fragment species can be responsible for ability of polyphenolic compounds to scavenge free radicals in the living cells. The gas-phase data were extrapolated to reactions in cellular environment by means of DFT calculations using polarizable continuum model approach. A molecular mechanism for antioxidant activity of polyphenolic compounds in proximity to the mitochondrial respiratory chain under conditions of excess negative charge was suggested. Namely, it is thought that molecular hydrogen, known for its selective antioxidant properties, can be efficiently generated via attachment of electrons (“leaked” from the respiratory chain into mitochondrial intermembrane space) to polyphenolic compound and may be responsible for its antioxidant activity. The corresponding negative fragment, i.e., quinone bearing an excess negative charge, can serve as electron carrier and can return the captured electron back to the respiration cycle. The number of hydroxyl substituents and their relative positions on aromatic rings of polyphenolic molecule are crucial for the present molecular mechanism, because these properties determine dissociative electron attachment cross-section.