Therapy of BRAF-mutant melanoma with selective inhibitors of BRAF (BRAFi) and MEK (MEKi) represents a major clinical advance but acquired resistance to therapy has emerged as a key obstacle. To date, no clinical approaches successfully resensitize to BRAF/MEK inhibition. Here, we develop a therapeutic strategy for melanoma using bromosporine, a bromodomain inhibitor. Bromosporine (bromo) monotherapy produced significant anti-tumor effects against established melanoma cell lines and patient-derived xenografts (PDXs). Combinatorial therapy involving bromosporine and cobimetinib (bromo/cobi) showed synergistic anti-tumor effects in multiple BRAFi-resistant PDX models. The bromo/cobi combination was superior in vivo to standard BRAFi/MEKi therapy in the treatment-naive BRAF-mutant setting and to MEKi alone in the setting of immunotherapy-resistant NRAS- and NF1-mutant melanoma. RNA sequencing of xenografts treated with bromo/cobi revealed profound down-regulation of genes critical to cell division and mitotic progression. Bromo/cobi treatment resulted in marked DNA damage and cell-cycle arrest, resulting in induction of apoptosis. These studies introduce bromodomain inhibition, alone or combined with agents targeting the mitogen activated protein kinase pathway, as a rational therapeutic approach for melanoma refractory to standard targeted or immunotherapeutic approaches.