The rationale behind targeted molecular therapy in cancer, oncogene addiction, is that tumors rely on driver oncogenes to control their proliferation and survival. Therefore, an efficacious targeted therapy should induce a dual, detrimental response to the tumor. While there have been clinical success stories using targeted therapies, even tumors that are initially sensitive invariably develop resistance. In the case of triple negative breast cancer (TNBC), despite extensive evidence pointing to its driver oncogene status, inhibitors of the Epidermal Growth Factor Receptor (EGFR) are considered clinically inefficacious. Resistance to EGFR inhibition has been predominantly described as due to genetic alterations. Yet it remains unclear why patients exhibiting the same dysregulated status of a driver oncogene react to targeted therapy, as in the case of EGFR-mutant non-small cell lung cancer, while others do not at all (i.e., TNBC). Furthermore, not all of resistance can be described by genetic alterations to EGFR, to its pathway effectors, or to compensatory pathways. Emerging data reveals that drugs can induce resistance by rewiring epigenomic, transcriptional, and translational regulatory mechanisms. Unfortunately, a major limitation in designing efficacious treatments is our inability to predict whether cell types can rewire in response to drug exposure. Therefore, it is necessary to elucidate mechanisms of growth and survival in cells that have undergone rewiring. This study characterized intrinsic resistance to EGFR inhibition in TNBC. We found that EGFR inhibition induces rewiring, which results in a resistant growth state that bypasses the EGFR-MAPK pathway as a whole. Additionally, we found that a tRNA-modifying complex masks the oncogene addiction status of EGFR in TNBC by stabilizing the protein abundance of a pro-survival protein. Importantly, this happens solely in the context of EGFR inhibition. Taken together, this study highlights potential therapeutic strategies for TNBC and strategies that can be used to improve our understanding of targeted therapy resistance, especially intrinsic resistance.