The relationship between corporate income tax rates and innovation is a critical international issue. Existing studies often overlook the potential mechanisms of market competition and productivity heterogeneity. This paper addresses these gaps by integrating these elements into a unified mathematical analysis framework. Using China's corporate income tax reform as a quasi-natural experiment, this study empirically tests the model. The findings reveal that decreases in tax rates significantly foster innovation, while increases have the opposite effect. The underlying mechanism involves market competition, with the impact of tax changes being more pronounced in firms with higher productivity. This study deepens the understanding of the nexus between corporate income tax and innovation, providing new insights to refine tax policies that promote innovative economic development globally.