Access to DNA packaged in nucleosomes is critical for gene regulation, DNA replication and DNA repair. In humans, the UV-damaged DNA-binding protein (UV-DDB) complex detects UV-light-induced pyrimidine dimers throughout the genome; however, it remains unknown how these lesions are recognized in chromatin, in which nucleosomes restrict access to DNA. Here we report cryo-electron microscopy structures of UV-DDB bound to nucleosomes bearing a 6-4 pyrimidine-pyrimidone dimer or a DNA-damage mimic in various positions. We find that UV-DDB binds UV-damaged nucleosomes at lesions located in the solvent-facing minor groove without affecting the overall nucleosome architecture. In the case of buried lesions that face the histone core, UV-DDB changes the predominant translational register of the nucleosome and selectively binds the lesion in an accessible, exposed position. Our findings explain how UV-DDB detects occluded lesions in strongly positioned nucleosomes, and identify slide-assisted site exposure as a mechanism by which high-affinity DNA-binding proteins can access otherwise occluded sites in nucleosomal DNA.