The objective of “low-carbon supply chain” and the development of e-commerce platforms (as e-platform) has boosted the production and sales of low-carbon products. Although the e-platform’s involvement promotes the efficiency of low-carbon products circulation, it leads to channel competition and double marginalization. To mitigate these negative effects, in the context of low-carbon production, a three-player supply chain that contains a low-carbon manufacturer, an e-platform, and a retailer are investigated. By introducing the Stackelberg game and cooperative game theory, the supply chain is coordinated under a cooperative framework considering the commission rate of e-platforms. Subsequently, Mathematica is used for numerical simulation. The results show that intensified channel competition and excessive commission rates will lead to malicious price cuts by supply chain members, which is not conducive to the low-carbon production of manufacturers. Appropriate cooperation strategies can improve the value and identity of low-carbon products and optimize the supply chain system. For coordination of supply chain, three cooperative game-theoretic mechanisms can coordinate low-carbon dual-channel supply chain of the e-commerce platform (LCDESC) well under different situations. These findings provide managerial insights for managers of LCDESC.