Unsupervised domain adaptive classification intends to improve the classification performance on unlabeled target domain. To alleviate the adverse effect of domain shift, many approaches align the source and target domains in the feature space. However, a feature is usually taken as a whole for alignment without explicitly making domain alignment proactively serve the classification task, leading to sub-optimal solution. The paper proposes an effective Task-oriented Alignment (ToAlign) for unsupervised domain adaptation (UDA), studies what features should be aligned across domains, and proposes to make the domain alignment proactively serve classification by performing feature decomposition and alignment under the guidance of the prior knowledge induced from the classification task itself. Particularly, the authors explicitly decompose a feature in the source domain into a task-related/discriminative feature that should be aligned, and a task-irrelevant feature that should be avoided/ignored, based on the classification meta-knowledge. Extensive experimental results on various benchmarks (e.g., Offce-Home, Visda-2017, and DomainNet) under different domain adaptation settings demonstrate the effectiveness of ToAlign which helps achieve the state-of-the-art performance.