While multiple mechanisms of BRAF^V600-mutant melanoma resistance to targeted MAPK signaling inhibitors (MAPKi) have been reported, the epigenetic regulation of this process remains undetermined. Here, using a CRISPR–Cas9 screen targeting chromatin regulators, we discover that haploinsufficiency of the histone deacetylase SIRT6 allows melanoma cell persistence in the presence of MAPKi. Haploinsufficiency, but not complete loss of SIRT6 promotes IGFBP2 expression via increased chromatin accessibility, H3K56 acetylation at the IGFBP2 locus, and consequent activation of the IGF-1 receptor (IGF-1R) and downstream AKT signaling. Combining a clinically applicable IGF-1Ri with BRAFi overcomes resistance of SIRT6 haploinsufficient melanoma cells in vitro and in vivo. Using matched melanoma samples derived from patients receiving dabrafenib + trametinib, we identify IGFBP2 as a potential biomarker for MAPKi resistance. Our study has not only identified an epigenetic mechanism of drug resistance, but also provides insights into a combinatorial therapy that may overcome resistance to standard-of-care therapy for BRAF^V600-mutant melanoma patients.