The emerging low rank matrix approximation (LRMA) method provides an energy efficient scheme for data collection in wireless sensor networks (WSNs) by randomly sampling a subset of sensor nodes for data sensing. However, the existing LRMA based methods generally underutilize the spatial or temporal correlation of the sensing data, resulting in uneven energy consumption and thus shortening the network lifetime. In this paper, we propose a correlated spatio-temporal data collection method for WSNs based on LRMA. In the proposed method, both the temporal consistence and the spatial correlation of the sensing data are simultaneously integrated under a new LRMA model. Moreover, the network energy consumption issue is considered in the node sampling procedure. We use Gini index to measure both the spatial distribution of the selected nodes and the evenness of the network energy status, then formulate and resolve an optimization problem to achieve optimized node sampling. The proposed method is evaluated on both the simulated and real wireless networks and compared with state-of-the-art methods. The experimental results show the proposed method efficiently reduces the energy consumption of network and prolongs the network lifetime with high data recovery accuracy and good stability.