BRCA1 is a tumor suppressor frequently mutated in breast and ovarian cancer, serving it as a target for therapeutic exploitation. Here, we show that BRCA1 has a synthetic lethality interaction with an epigenetics regulator, bromodomain and extra-terminal domain (BET). BET inhibition led to gene expression changes reversing MYC-dependent transcription repression of a redox regulator, thioredoxin-interacting protein (TXNIP), via switching the promoter occupant from MYC to MondoA:MLX complex. Reversing the MYC-TXNIP axis inhibited thioredoxin activity and elevated cellular oxidative stress, causing DNA damages that are detrimental to BRCA1-deficient breast cancer cells. Tumor xenograft models and breast cancer clinical data analyses further demonstrated an in vivo synthetic lethality interaction and clinical association between BET/TXNIP and BRCA1 deficiency in the survival of breast cancer patients.