The human genome is folded into regulatory units termed ‘topologically-associated domains’ (TADs). Genome-wide studies support a global role for the insulator protein CTCF in mediating chromosomal looping and the topological constraint of TAD boundaries. However, the impact of individual insulators on enhancer-gene interactions and transcription remains poorly understood. Here, we investigate epigenome editing strategies for perturbing individual CTCF insulators and evaluating consequent effects on genome topology and transcription. We show that fusions of catalytically-inactive Cas9 (dCas9) to transcriptional repressors (dCas9-KRAB) and DNA methyltransferases (dCas9-DNMT3A, dCas9-DNMT3A3L) can selectively displace CTCF from specific insulators, but only when precisely targeted to the cognate motif. We further demonstrate that stable, partially-heritable insulator disruption can be achieved through combinatorial hit-and-run epigenome editing. Finally, we apply these strategies to simulate an insulator loss mechanism implicated in brain tumorigenesis. Our study provides strategies for stably modifying genome organization and gene activity without altering the underlying DNA sequence.