Tooth segmentation in Cone-Beam Computed Tomography (CBCT) remains challenging, especially for fine structures like root apices, which is critical for assessing root resorption in orthodontics. We introduce GEPAR3D, a novel approach that unifies instance detection and multi-class segmentation into a single step tailored to improve root segmentation. Our method integrates a Statistical Shape Model of dentition as a geometric prior, capturing anatomical context and morphological consistency without enforcing restrictive adjacency constraints. We leverage a deep watershed method, modeling each tooth as a continuous 3D energy basin encoding voxel distances to boundaries. This instance-aware representation ensures accurate segmentation of narrow, complex root apices. Trained on publicly available CBCT scans from a single center, our method is evaluated on external test sets from two in-house and two public medical centers. GEPAR3D achieves the highest overall segmentation performance, averaging a Dice Similarity Coefficient (DSC) of 95.0% (+2.8% over the second-best method) and increasing recall to 95.2% (+9.5%) across all test sets. Qualitative analyses demonstrated substantial improvements in root segmentation quality, indicating significant potential for more accurate root resorption assessment and enhanced clinical decision-making in orthodontics. We provide the implementation and dataset at https://github.com/tomek1911/GEPAR3D.