The low-carbon cooperation between providers and demanders is one of the ways to achieve sustainable development in cloud manufacturing, which has become an important issue. However, the effective ways for the cloud platform to encourage such cooperation are unclear. Considering the low-carbon strategies of the supply and demand sides and the regulation of the cloud platform, an evolutionary game model involving service providers, service demanders, and the cloud platform is established, and the tripartite evolutionary stability is discussed. Further, the impacts of important factors, such as regulatory costs, on the tripartite strategies are analyzed through numerical simulation. The results illustrate that the cloud platform reasonably optimizes the rewards and penalties for low-carbon cooperation to promote the enthusiastic participation of service providers and demanders. The cloud platform can set penalties (rewards) for providers based on their low-carbon costs and rewards (penalties). Additionally, the low-carbon costs of service providers and the additional costs of demanders negatively affect the low-carbon cooperation between providers and demanders. Meanwhile, the low-carbon costs and additional costs for the providers and demanders to engage in low-carbon cooperation are affected by the rewards and penalties of the cloud platform. The results could provide insights into the game decisions of the supply and demand sides and the cloud platform, facilitating sustainable supply chain advancement.