Mutations in BRAF activate oncogenic MAPK signalling in almost half of cutaneous melanomas. Inhibitors of BRAF (BRAFi) and its target MEK are widely used to treat melanoma patients with BRAF mutations but unfortunately acquired resistance occurs in the majority of patients. Resistance results from mutations or non-genomic changes that either reactivate MAPK signalling or activate other pathways that provide alternate survival and growth signalling. Here, we show the histone deacetylase inhibitor (HDACi) panobinostat overcomes BRAFi resistance in melanoma, but this is dependent on the resistant cells showing a partial response to BRAFi treatment. Using patient- and in vivo-derived melanoma cell lines with acquired BRAFi resistance, we show that combined treatment with the BRAFi encorafenib and HDACi panobinostat in 2D and 3D culture systems synergistically induced caspase-dependent apoptotic cell death. Key changes induced by HDAC inhibition included decreased PI3K pathway activity associated with a reduction in the protein level of a number of receptor tyrosine kinases, and cell line dependent upregulation of pro-apoptotic BIM or NOXA together with reduced expression of anti-apoptotic proteins. Independent of these changes, panobinostat reduced c-Myc and pre-treatment of cells with siRNA against c-Myc reduced BRAFi/HDACi drug-induced cell death. These results suggest that a combination of HDAC and MAPK inhibitors may play a role in treatment of melanoma where the resistance mechanisms are due to activation of MAPK-independent pathways.