Acquiring complete point clouds for real-world scenarios is labor-intensive, making it impractical for conventional learning-based approaches. Numerous methods have been proposed to overcome this limitation by leveraging synthetic complete point clouds. While access to complete point clouds offers a notable advantage, they often struggle to bridge domain gaps, leading to sub-optimal performance. As a remedy, we propose a novel part-based framework for synthetic-to-real domain adaptation in point cloud completion. Our approach starts on the observation that domain gaps inherent in part information are relatively small, as parts are shared properties across categories regardless of domains. To employ part-based approach to point cloud completion, we introduce Part-Based Decomposition (PBD) module to generate part input point clouds. Subsequently, we design a Part-Aware Completion (PAC) module, which operates in a part-wise manner to produce complete point clouds. Within PAC, we devise a novel part-aware transformer to learn relationships between parts and utilize this information to infer missing parts in incomplete point clouds. Extensive experiments demonstrate that our part-based framework significantly outperforms existing studies on real-world point cloud datasets.