Mammalian SWI/SNF chromatin remodelling complexes exist in three distinct, final-form assemblies: canonical BAF (cBAF), PBAF and a newly characterized non-canonical complex (ncBAF). However, their complex-specific targeting on chromatin, functions and roles in disease remain largely undefined. Here, we comprehensively mapped complex assemblies on chromatin and found that ncBAF complexes uniquely localize to CTCF sites and promoters. We identified ncBAF subunits as synthetic lethal targets specific to synovial sarcoma and malignant rhabdoid tumours, which both exhibit cBAF complex (SMARCB1 subunit) perturbation. Chemical and biological depletion of the ncBAF subunit, BRD9, rapidly attenuates synovial sarcoma and malignant rhabdoid tumour cell proliferation. Importantly, in cBAF-perturbed cancers, ncBAF complexes maintain gene expression at retained CTCF-promoter sites and function in a manner distinct from fusion oncoprotein-bound complexes. Together, these findings unmask the unique targeting and functional roles of ncBAF complexes and present new cancer-specific therapeutic targets.