Breast cancer cells with stem-like properties are critical for tumor progression, yet much about these cells remains unknown. Here, we characterize a population of stem-like breast cancer cells expressing the integrin αvβ3 as transcriptionally related to activated stem/basal cells in the normal human mammary gland. An unbiased functional screen of genes unique to these cells identified the matrix protein TGFBI (BIG-H3) and the transcription factor ZEB1 as necessary for tumorsphere formation. Surprisingly, these genes were not required for cell proliferation or survival, but instead maintained chromosomal stability. Consistent with this finding, CRISPR deletion of either gene synergized with PARP inhibition to deplete αvβ3+ stem-like cells, which are normally resistant to this therapy. Our findings highlight a critical role for TGFBI-ZEB1 protection against genetic stress as a key attribute of activated stem-like cells and suggest that disrupting this ability may enhance their "BRCAness" by increasing sensitivity to PARP inhibitors.