Domain gap between synthetic and real data in visual regression (e.g., 6D pose estimation) is bridged in this paper via global feature alignment and local refinement on the coarse classification of discretized anchor classes in target space, which imposes a piece-wise target manifold regularization into domain-invariant representation learning. Specifically, our method incorporates an explicit self-supervised manifold regularization, revealing consistent cumulative target dependency across domains, to a self-training scheme (e.g., the popular Self-Paced Self-Training) to encourage more discriminative transferable representations of regression tasks. Moreover, learning unified implicit neural functions to estimate relative direction and distance of targets to their nearest class bins aims to refine target classification predictions, which can gain robust performance against inconsistent feature scaling sensitive to UDA regressors. Experiment results on three public benchmarks of the challenging 6D pose estimation task can verify the effectiveness of our method, consistently achieving superior performance to the state-of-the-art for UDA on 6D pose estimation. Codes and pre-trained models are available https://github.com/Gorilla-Lab-SCUT/MAST.