Climate change is emerging as a significant threat to sustainable human development in the coming decades, and the thirteenth of the United Nations' Sustainable Development Goals (SDGs) aims precisely to mitigate this threat through practical action. We employ a composite system synergy model to measure the synergy between China's industrial and innovation chains and explore pathways for listed enterprises to achieve carbon neutrality in pursuit of SDGs. The findings reveal an upward trend in the synergistic degree of China's industrial and innovation chains, with a greater degree observed in the eastern regions. The combined development of the two chains demonstrates an ability to mitigate the intensity of carbon emissions across enterprises through digital advancements and advancements in green technology. Additionally, disparities in geographical location, the degree of marketisation, the nature of enterprise equity, and pollution levels of enterprises are found to exert asymmetric effects on carbon emissions. Moreover, green finance emerges as a significant mediator in enhancing the inhibitory effect of dual-chain synergy on enterprise carbon emission intensity. Our results trigger important policy narratives: a coupling of interaction between the government and the market can deliver carbon neutrality and facilitate a steadfast transition to a low-carbon economy for businesses.