Embedding plays a key role in modern recommender systems because they are virtual representations of real-world entities and the foundation for subsequent decision-making models. In this paper, we propose a novel embedding update mechanism, Structure-aware Embedding Evolution (SEvo for short), to encourage related nodes to evolve similarly at each step. Unlike GNN (Graph Neural Network) that typically serves as an intermediate module, SEvo is able to directly inject graph structural information into embedding with minimal computational overhead during training. The convergence properties of SEvo along with its potential variants are theoretically analyzed to justify the validity of the designs. Moreover, SEvo can be seamlessly integrated into existing optimizers for state-of-the-art performance. Particularly SEvo-enhanced AdamW with moment estimate correction demonstrates consistent improvements across a spectrum of models and datasets, suggesting a novel technical route to effectively utilize graph structural information beyond explicit GNN modules.