In this work, we leverage estimated depth to boost self-supervised contrastive learning for segmentation of urban scenes, where unlabeled videos are readily available for training self-supervised depth estimation. We argue that the semantics of a coherent group of pixels in 3D space is self-contained and invariant to the contexts in which they appear. We group coherent, semantically related pixels into coherent depth regions given their estimated depth and use copy-paste to synthetically vary their contexts. In this way, cross-context correspondences are built in contrastive learning and a context-invariant representation is learned. For unsupervised semantic segmentation of urban scenes, our method surpasses the previous state-of-the-art baseline by +7.14% in mIoU on Cityscapes and +6.65% on KITTI. For fine-tuning on Cityscapes and KITTI segmentation, our method is competitive with existing models, yet, we do not need to pre-train on ImageNet or COCO, while we are also more computationally efficient. Our code is available on https://github.com/LeungTsang/CPCDR.@en