Single-strand breaks (SSBs) are one of the most prevalent forms of DNA damage found in the chromatinized genome and are repaired by direct single-strand break repair (SSBR) or base excision repair (BER). DNA polymerase beta (Pol β) is the primary enzyme responsible for processing the 1-nt gap intermediate in chromatin during SSBR and BER. However, the mechanism used by Pol β to process a 1-nt gap in the context of the nucleosome and chromatin remains poorly understood. Here, we use biochemical assays and cryogenic electron microscopy (cryo-EM) to determine the kinetic and structural basis of gap-filling DNA synthesis in the nucleosome by Pol β. Kinetic analysis identified that gap-filling DNA synthesis in the nucleosome by Pol β is position-dependent, where solvent exposed 1-nt gaps are processed more efficiently than histone-occluded 1-nt gaps. A series of cryo-EM structures of Pol β bound to a solvent-exposed 1-nt gap in the nucleosome reveal a global DNA sculpting mechanism for 1-nt gap recognition, which is mediated by sequential engagement of the Pol β lyase domain and polymerase domain. Finally, cryo-EM structures of Pol β bound to 1-nt gaps at two additional positions in the nucleosomal DNA define the structural basis for position-dependent nucleotide insertion in the nucleosome. This work establishes the mechanism used by Pol β for processing 1-nt gaps in the nucleosome during SSBR and BER, providing fundamental insight into DNA repair in chromatin.