Encouraging enterprises to adopt green and low-carbon technological innovation is an important measure to cope with climate change and achieve low-carbon economic development. As the main stakeholders of green and low-carbon technological innovation of enterprises, what measures should the government and the public take to encourage green and low-carbon technological innovation of enterprises has become one of the focuses of research. This study constructs a tripartite evolutionary game model among the government, the public, and enterprises and then obtains the evolutionary stability strategy by analyzing the replication dynamic equation of each subject. Numerical simulation is made on the evolution path of the game under different enforcement intensities of environmental regulation means. The result shows that pollution tax, low-carbon technology innovation subsidy, and environmental protection publicity and guidance are three environmental regulation means to effectively stimulate enterprises’ green and low-carbon technology innovation. And moderate pollution tax, low-intensity publicity of public environmental protection, and high innovation incentive compensation have the highest incentive efficiency for enterprises’ green and low-carbon technological innovation. Targeted suggestions for promoting green and low-carbon technological innovation of enterprises are put forward in the end.