With the proposal of China’s dual-carbon goal, the contradiction between regional economic development, energy consumption, and environmental governance is increasingly acute, and the stability of the economy-energy-environment (3E) system is increasingly prominent, which is an inevitable choice to effectively promote the green and low-carbon transformation of China’s economy. Based on the stability of the 3E system, an index system was constructed from three dimensions: availability of the energy-resource system, coordination of the energy-economic system, and sustainability of the energy-ecosystem. Based on the principal component analysis and mature-element extension evaluation model, the stability and spatio-temporal evolution characteristics of the 3E system in East China were systematically evaluated. The results show that, firstly, from the spatial dimension, the coordination degree of the energy economic system is good in the economically developed A region, while the energy utilization efficiency is low in the economically less developed B region, and the sustainability of the energy ecosystem is relatively poor. Secondly, in terms of time dimension, Jiangxi, Jiangsu, and Shandong are the regions with rising fluctuations, Shanghai and Anhui are the regions with decreasing fluctuations, and Zhejiang and Fujian are the regions with relatively stable fluctuations, which is conducive to realizing the common vision of regional green and low-carbon development, breaking the geographical and information gap between provinces, and gradually forming a community of 3E system coupling and coordinated development.