Evidence has long suggested that epidermal growth factor receptor (EGFR) may play a prominent role in triple-negative breast cancer (TNBC) pathogenesis, but clinical trials of EGFR inhibitors have yielded disappointing results. Using a candidate drug screen, we identified that inhibition of cyclin-dependent kinases 12 and 13 (CDK12/13) dramatically sensitizes diverse models of TNBC to EGFR blockade. This combination therapy drives cell death through the 4E-BP1-dependent suppression of the translation and translation-linked turnover of driver oncoproteins, including MYC. A genome-wide CRISPR/Cas9 screen identified the CCR4-NOT complex as a major determinant of sensitivity to the combination therapy whose loss renders 4E-BP1 unresponsive to drug-induced dephosphorylation, thereby rescuing MYC translational suppression and promoting MYC stability. The central roles of CCR4-NOT and 4E-BP1 in response to the combination therapy were further underscored by the observation of CNOT1 loss and rescue of 4E-BP1 phosphorylation in TNBC cells that naturally evolved therapy resistance. Thus, pharmacological inhibition of CDK12/13 reveals a long-proposed EGFR dependence in TNBC that functions through the cooperative regulation of translation-coupled oncoprotein stability.