This paper tackles the task of emotion-cause pair extraction in the unsupervised domain adaptation setting.The problem is challenging as the distributions of the events causing emotions in target domains are dramatically different than those in source domains, despite the distributions of emotional expressions between domains are overlapped. Inspired by causal discovery,we propose a novel deep latent model in the variational autoencoder (VAE) framework, which not only captures the underlying latent structures of data but also utilizes the easily transferable knowledge of emotions as the bridge to link the distributions of events in different domains. To facilitate knowledge transfer across domains, we also propose a novel variational posterior regularization technique to disentangle the latent representations of emotions from those of events in order to mitigate the damage caused by the spurious correlations related to the events in source domains. Through extensive experiments, we demonstrate that our model outperforms the strongest baseline by approximately 11.05% on a Chinese benchmark and 2.45% on a English benchmark in terms of weighted-average F1 score. We have released our source code and the generated dataset publicly at: https://github.com/tk1363704/CAREL-VAE.