Ionizing radiation (IR) and reactive oxygen species (ROS)-induced oxidative stress can cause damage to cellular biomolecules, including DNA, proteins, and lipids. These harmful effects can compromise essential cellular functions and significantly raise the risk of metabolic dysfunction, accumulation of harmful mutations, genome instability, cancer, accelerated cellular senescence, and even death. Here, we present an investigation of HeLa cancer cells’ early response to gamma IR (γ-IR) and oxidative stress after preincubation of the cells with natural extracts of the resurrection plant Haberlea rhodopensis. In light of the superior protection offered by plant extracts against radiation and oxidative stress, we investigated the cellular defence mechanisms involved in such protection. Specifically, we sought to evaluate the molecular effects of H. rhodopensis extract (HRE) on cells subjected to genotoxic stress by examining the components of the redox pathway and quantifying the transcription levels of several critical genes associated with DNA repair, cell cycle regulation, and apoptosis. The influence of HRE on genome integrity and the cell cycle was also studied via comet assay and flow cytometry. Our findings demonstrate that HREs can effectively modulate the cellular response to genotoxic and oxidative stress within the first two hours following exposure, thereby reducing the severity of such stress. Furthermore, we observed the specificity of genoprotective HRE doses depending on the source of the applied genotoxic stress.