The protein kinase B-Raf proto-oncogene, serine/threonine kinase (BRAF) is an oncogenic driver and therapeutic target in melanoma. Inhibitors of BRAF (BRAFi) have shown high response rates and extended survival in patients with melanoma who bear tumors that express mutations encoding BRAF proteins mutant at Val600, but a vast majority of these patients develop drug resistance^{1, 2}. Here we show that loss of stromal antigen 2 (STAG2) or STAG3, which encode subunits of the cohesin complex, in melanoma cells results in resistance to BRAFi. We identified loss-of-function mutations in STAG2, as well as decreased expression of STAG2 or STAG3 proteins in several tumor samples from patients with acquired resistance to BRAFi and in BRAFi-resistant melanoma cell lines. Knockdown of STAG2 or STAG3 expression decreased sensitivity of BRAF^Val600Glu-mutant melanoma cells and xenograft tumors to BRAFi. Loss of STAG2 inhibited CCCTC-binding-factor-mediated expression of dual specificity phosphatase 6 (DUSP6), leading to reactivation of mitogen-activated protein kinase (MAPK) signaling (via the MAPKs ERK1 and ERK2; hereafter referred to as ERK). Our studies unveil a previously unknown genetic mechanism of BRAFi resistance and provide new insights into the tumor suppressor function of STAG2 and STAG3.