<p>Low-carbon transformation is a crucial component in promoting high-quality economic development. As China gradually adopts a multi-stakeholder governance model for low-carbon emission reductions, this paper integrates the key actors—government, Environmental Non-Governmental Organizations (ENGOs), enterprises, and the public—into a unified framework. A four-party evolutionary game model is developed based on Lyapunov's first method to analyze the stability of strategy choices among these actors. Numerical simulations are employed to explore how parameter changes influence the stable strategies of different stakeholders. The findings show that variations in enterprise low-carbon production costs, the regulatory costs of ENGOs, and public funding for low-carbon products all affect the time required for the system to reach a stable equilibrium. Stakeholders tend to choose strategies that yield positive net benefits. Rising low-carbon technology costs for enterprises delay system convergence and lead to inefficient equilibria. High supervision costs force ENGOs to adopt passive oversight, influencing government regulatory adjustments. While increasing public low-carbon consumption costs does not alter the final equilibrium, it accelerates the low-carbon transition for enterprises. The intensity of ENGOs' penalties is critical in the transition process, and enterprise subsidies for low-carbon consumption influence public behavior. Future research could further investigate complex multi-agent interactions and refine the model for dynamic policy scenarios.</p>