This paper proposes a coupled coordination model of low-carbon energy restructuring and regional economic growth based on stochastic optimization algorithm, revealing the dynamic association between the two. Based on the spatial autoregressive model, the influencing factors of regional economic growth are explored. The dynamic spatial panel data model integrating FMOLS and panel LM test is used to verify the reasonableness of the selection of indicators for the low carbon energy structure adjustment subsystem. Combined with the entropy method of weighting, the level of synergistic development is quantified relying on a coupled coordination analysis index system containing 6 energy indicators and 8 economic indicators. Based on the panel data of 15 provinces in China from 2020 to 2024, it is empirically found that the coupling degree of China’s low-carbon energy structural adjustment and regional economic growth is maintained at a high level of 0.89-0.99, while the degree of coordination is developed from near-dislocation recession zigzagging to intermediate coupling coordination, and the degree of the two coupling coordination is increased from 0.46 (near-dislocation) in 2020 to 0.79 (intermediate coordination). The study provides theoretical support for the formulation of regional differentiated energy policies and the realization of synergistic optimization of economic-energy-environmental systems.