The antioxidant activity of essential oils (EOs) is an important and frequently studied property, yet it is not sufficiently understood in terms of the contribution of EOs mixtures’ constituents and biological properties. In this study, a series of 61 commercial EOs were first evaluated as antioxidants in vitro, following as closely as possible the cellular pathways of reactive oxygen species (ROS) generation. Hence, EOs were assessed for the ability either to chelate metal ions, thus interfering with ROS generation within the respiratory chain, or to neutralize 2,2-diphenyl-1-picrylhydrazyl (DPPH•) and lipid peroxide radicals (LOO•), thereby halting lipid peroxidation, as well as to neutralize 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid cation radicals (ABTS•+) and hydroxyl radicals (OH•), thereby preventing the ROS species from damaging DNA nucleotides. Showing noteworthy potencies to neutralize all of the radicals at the ng/mL level, the active EOs were also characterized as protectors of DNA double strands from damage induced by peroxyl radicals (ROO•), emerging from 2,2′-azobis-2-methyl-propanimidamide (AAPH) as a source, and OH•, indicating some genome protectivity and antigenotoxicity effectiveness in vitro. The chemical compositions of the EOs associated with the obtained activities were then analyzed by means of machine learning (ML) classification algorithms to generate quantitative composition–activity relationships (QCARs) models (models published in the AI4EssOil database available online). The QCARs models enabled us to highlight the key features (EOSs’ chemical compounds) for exerting the redox potencies and to define the partial dependencies of the features, viz. percentages in the mixture required to exert a given potency. The ML-based models explained either the positive or negative contribution of the most important chemical components: limonene, linalool, carvacrol, eucalyptol, α-pinene, thymol, caryophyllene, p-cymene, eugenol, and chrysanthone. Finally, the most potent EOs in vitro, Ylang-ylang (Cananga odorata (Lam.)) and Ceylon cinnamon peel (Cinnamomum verum J. Presl), were promptly administered in vivo to evaluate the rescue ability against redox damage caused by CCl4, thereby verifying their antioxidant and antigenotoxic properties either in the liver or in the kidney.