Precise event spotting (PES) aims to recognize fine-grained events at exact moments and has become a key component of sports analytics. This task is particularly challenging due to rapid succession, motion blur, and subtle visual differences. Consequently, most existing methods rely on domain-specific, end-to-end training with large labeled datasets and often struggle in few-shot conditions due to their dependence on pixel- or pose-based inputs alone. However, obtaining large labeled datasets is practically hard. We propose a Unified Multi-Entity Graph Network (UMEG-Net) for few-shot PES. UMEG-Net integrates human skeletons and sport-specific object keypoints into a unified graph and features an efficient spatio-temporal extraction module based on advanced GCN and multi-scale temporal shift. To further enhance performance, we employ multimodal distillation to transfer knowledge from keypoint-based graphs to visual representations. Our approach achieves robust performance with limited labeled data and significantly outperforms baseline models in few-shot settings, providing a scalable and effective solution for few-shot PES. Code is publicly available at https://github.com/LZYAndy/UMEG-Net.