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Breast and mammary epithelial cells experience different local environments during tissue development and tumorigenesis. Microenvironmental heterogeneity gives rise to distinct cell regulatory states whose identity and importance are just beginning to be appreciated. Cellular states diversify when clonal three-dimensional (3D) spheroids are cultured in basement membrane, and one such state is associated with stress tolerance and poor response to anticancer therapeutics. Here, we found that this state was jointly coordinated by the NRF2 and p53 pathways, which were costabilized by spontaneous oxidative stress within 3D cultures. Inhibition of NRF2 or p53 individually disrupted some of the transcripts defining the regulatory state but did not yield a notable phenotype in nontransformed breast epithelial cells. In contrast, combined perturbation prevented 3D growth in an oxidative stress–dependent manner. By integrating systems models of NRF2 and p53 signaling in a single oxidative stress network, we recapitulated these observations and made predictions about oxidative stress profiles during 3D growth. NRF2 and p53 signaling were similarly coordinated in normal breast epithelial tissue and hormone-negative ductal carcinoma in situ lesions but were uncoupled in triple-negative breast cancer (TNBC), a subtype in which p53 is usually mutated. Using the integrated model, we correlated the extent of this uncoupling in TNBC cell lines with the importance of NRF2 in the 3D growth of these cell lines and their predicted handling of oxidative stress. Our results point to an oxidative stress tolerance network that is important for single cells during glandular development and the early stages of breast cancer.