Ubiquitin-mediated proteolysis is a fundamental mechanism used by eukaryotic cells to maintain homeostasis and protein quality, and to control timing in biological processes. Two essential aspects of ubiquitin regulation are conjugation through E1-E2-E3 enzymatic cascades, and recognition by ubiquitin-binding domains. An emerging theme in the ubiquitin field is that these two properties are often amalgamated in conjugation enzymes. In addition to covalent thioester linkage to ubiquitin's C-terminus for ubiquitin transfer reactions, conjugation enzymes often bind non-covalently and weakly to ubiquitin at "exosites". However, identification of such sites is typically empirical and particularly challenging in large molecular machines. Here, studying the 1.2 MDa E3 ligase Anaphase-Promoting Complex/Cyclosome (APC/C), which controls cell division and many aspects of neurobiology, we discover a method for identifying unexpected ubiquitin-binding sites. Using a panel of ubiquitin variants (UbVs) we identify a protein-based inhibitor that blocks ubiquitin ligation to APC/C substrates in vitro and ex vivo. Biochemistry, NMR, and cryo EM structurally define the UbV interaction, explain its inhibitory activity through binding the surface on the APC2 subunit that recruits the E2 enzyme UBE2C, and ultimately reveal that this APC2 surface is also a ubiquitin-binding exosite with preference for K48-linked chains. The results provide a new tool for probing APC/C activity, have implications for the coordination of K48-linked Ub chain binding by APC/C with the multistep process of substrate polyubiquitylation, and demonstrate the power of UbV technology for identifying cryptic ubiquitin binding sites within large multiprotein complexes.