Unsupervised Graph Domain Adaptation (UGDA) seeks to bridge distribution shifts between domains by transferring knowledge from labeled source graphs to given unlabeled target graphs. Existing UGDA methods primarily focus on aligning features in the latent space learned by graph neural networks (GNNs) across domains, often overlooking structural shifts, resulting in limited effectiveness when addressing structurally complex transfer scenarios. Given the sensitivity of GNNs to local structural features, even slight discrepancies between source and target graphs could lead to significant shifts in node embeddings, thereby reducing the effectiveness of knowledge transfer. To address this issue, we introduce a novel approach for UGDA called Target-Domain Structural Smoothing (TDSS). TDSS is a simple and effective method designed to perform structural smoothing directly on the target graph, thereby mitigating structural distribution shifts and ensuring the consistency of node representations. Specifically, by integrating smoothing techniques with neighborhood sampling, TDSS maintains the structural coherence of the target graph while mitigating the risk of over-smoothing. Our theoretical analysis shows that TDSS effectively reduces target risk by improving model smoothness. Empirical results on three real-world datasets demonstrate that TDSS outperforms recent state-of-the-art baselines, achieving significant improvements across six transfer scenarios. The code is available in https://github.com/cwei01/TDSS.