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In order to explore the impact of a manufacturer’s or retailer’s undertaking corporate social responsibility (CSR) and different power structures on their joint green marketing decisions and profits in the green supply chain, this paper establishes green supply chain optimization models under six different decision-making scenarios according to two different CSR bearers and three different power structures. Based on the main assumptions of a linear product demand function and CSR measured by consumer surplus, this paper solves the equilibrium solutions of the manufacturer and the retailer through game theory. The results show that: First, the difference in the degree of CSR undertaken by manufacturers and retailers leads to a difference in the ranking of optimal strategies of both parties under the three power structures. Second, under the same power structure, compared with undertaking CSR by oneself, when the other party undertakes CSR, the level of the product’s green degree, the level of green promotion, the party’s own profit, and the profit of the other party are all higher. Third, regardless of the power structure, manufacturers and retailers undertaking CSR is conducive to improving the level of product greenness, increasing green promotion, lowering the retail price, increasing consumers’ willingness to buy green products, and ultimately helping to increase the profits of manufacturers and retailers.