Epigenetic aberrations are widespread in cancer, yet the underlying mechanisms and causality remain poorly understood. A subset of gastrointestinal stromal tumours (GISTs) lack canonical kinase mutations but instead have succinate dehydrogenase (SDH) deficiency and global DNA hyper-methylation. Here, we associate this hyper-methylation with changes in genome topology that activate oncogenic programs. To investigate epigenetic alterations systematically, we mapped DNA methylation, CTCF insulators, enhancers, and chromosome topology in KIT-mutant, PDGFRA-mutant and SDH-deficient GISTs. Although these respective subtypes shared similar enhancer landscapes, we identified hundreds of putative insulators where DNA methylation replaced CTCF binding in SDH-deficient GISTs. We focused on a disrupted insulator that normally partitions a core GIST super-enhancer from the FGF4 oncogene. Recurrent loss of this insulator alters locus topology in SDH-deficient GISTs, allowing aberrant physical interaction between enhancer and oncogene. CRISPR-mediated excision of the corresponding CTCF motifs in an SDH-intact GIST model disrupted the boundary between enhancer and oncogene, and strongly upregulated FGF4 expression. We also identified a second recurrent insulator loss event near the KIT oncogene, which is also highly expressed across SDH-deficient GISTs. Finally, we established a patient-derived xenograft (PDX) from an SDH-deficient GIST that faithfully maintains the epigenetics of the parental tumour, including hypermethylation and insulator defects. This PDX model is highly sensitive to FGF receptor (FGFR) inhibition, and more so to combined FGFR and KIT inhibition, validating the functional significance of the underlying epigenetic lesions. Our study reveals how epigenetic alterations can drive oncogenic programs in the absence of canonical kinase mutations, with implications for mechanistic targeting of aberrant pathways in cancers.