The antioxidant action of terngymnoside C (1) and hydroxytyrosol-1-glucoside (2), isolated for the first time from the flower buds of Ternstroemia lineata, as well as katsumadin (3), obtained from the seedless fruits, was evaluated using ABTS^•+ and H₂O₂–Saccharomyces cerevisiae models. In silico docking analysis of 1, 2, and 3 determined their affinity forces to the aquaporin monomers of the modeled S. cerevisiae protein 3 (AQP3) and human protein 7 (AQP7) channels that regulate the H₂O₂ cell transport. The ABTS^•+ antiradical capacity of these compounds showed IC₅₀ values of 22.00 μM (1), 47.64 μM (2), and 73.93 μM (3). The S. cerevisiae antioxidant assay showed that at 25 µM (1) and 50 µM (2 and 3), the cells were protected from H₂O₂-oxidative stress. These compounds, together with quercetin and vitamin C, were explored through the modeled S. cerevisiae AQP3 and human AQP7 by molecular docking analysis. To explain these results, an antioxidant mechanism for the isolated compounds was proposed through blocking H₂O₂ passage mediated by aquaporin transport. On the other hand, 1, 2, and 3 were not cytotoxic in a panel of three cancer cell lines.