Source-Free Domain Adaptation (SFDA) aims to adapt a pre-trained model from an annotated source domain to an unlabelled target domain without accessing the source data, thereby preserving data privacy. While existing SFDA methods have proven effective in reducing reliance on source data, they struggle to perform well on multivariate time series (MTS) due to their failure to consider the intrinsic spatial correlations inherent in MTS data. These spatial correlations are crucial for accurately representing MTS data and preserving invariant information across domains. To address this challenge, we propose Temporal Restoration and Spatial Rewiring (TERSE), a novel and concise SFDA method tailored for MTS data. Specifically, TERSE comprises a customized spatial-temporal feature encoder designed to capture the underlying spatial-temporal characteristics, coupled with both temporal restoration and spatial rewiring tasks to reinstate latent representations of the temporally masked time series and the spatially masked correlated structures. During the target adaptation phase, the target encoder is guided to produce spatially and temporally consistent features with the source domain by leveraging the source pre-trained temporal restoration and spatial rewiring networks. Therefore, TERSE can effectively model and transfer spatial-temporal dependencies across domains, facilitating implicit feature alignment. In addition, as the first approach to simultaneously consider spatial-temporal consistency in MTS-SFDA, TERSE can also be integrated as a versatile plug-and-play module into established SFDA methods. Extensive experiments on three real-world time series datasets demonstrate the effectiveness and versatility of our approach.