A major challenge in cancer genomics is to identify genes with functional roles in cancer and uncover their mechanisms of action. We introduce an integrative framework that identifies cancer-relevant genes by pinpointing those whose interaction or other functional sites are enriched in somatic mutations across tumors. We derive analytical calculations that enable us to avoid time-prohibitive permutation-based significance tests, making it computationally feasible to simultaneously consider multiple measures of protein site functionality. Our accompanying software, PertInInt, combines knowledge about sites participating in interactions with DNA, RNA, peptides, ions, or small molecules with domain, evolutionary conservation, and gene-level mutation data. When applied to 10,037 tumor samples, PertInInt uncovers both known and newly predicted cancer genes, while additionally revealing what types of interactions or other functionalities are disrupted. PertInInt's analysis demonstrates that somatic mutations are frequently enriched in interaction sites and domains and implicates interaction perturbation as a pervasive cancer-driving event.