Power batteries, the core component of the rapidly evolving electric vehicle industry, have increasingly become a focal point of attention. Recycling power batteries can mitigate environmental pollution and utilize resources efficiently, which is crucial for fostering a low-carbon economy and achieving sustainable development. Utilizing prospect theory, this study proposes a tripartite game model for low-carbon innovation in power battery recycling, involving government agencies, power battery manufacturers, and recycling enterprises. This paper initially identifies the evolutionary stability strategy, subsequently simulates the evolutionary process through parameter assignment, and explores parameter sensitivity along with comparative effects. This study indicates the following: (i) Government incentives are pivotal in motivating manufacturers and recyclers towards low-carbon innovation. (ii) Reducing technology costs and enhancing spillovers significantly boost low-carbon innovation’s appeal. (iii) Moderate carbon taxes can encourage businesses to engage in low-carbon innovation, while excessively high taxes may increase operating costs and hinder investment in innovation. Lastly, policy recommendations are made in order to support environmental preservation and the industry’s sustainable growth in the power battery recycling sector.