For unsupervised domain adaptation problems, the strategy of aligning the two domains in latent feature space through adversarial learning has achieved much progress in image classification, but usually fails in semantic segmentation tasks in which the latent representations are overcomplex. In this work, we equip the adversarial network with a "significance-aware information bottleneck (SIB)", to address the above problem. The new network structure, called SIBAN, enables a significance-aware feature purification before the adversarial adaptation, which eases the feature alignment and stabilizes the adversarial training course. In two domain adaptation tasks, i.e., GTA5 -> Cityscapes and SYNTHIA -> Cityscapes, we validate that the proposed method can yield leading results compared with other feature-space alternatives. Moreover, SIBAN can even match the state-of-the-art output-space methods in segmentation accuracy, while the latter are often considered to be better choices for domain adaptive segmentation task.