The “14th Five-Year” development plan of the construction industry of the Chinese government makes it clear that intelligent buildings are the general direction of future construction development. However, the occurrence of construction accidents in recent years has brought huge casualties. With the rapid development of third-party inspection institutions, their judgment has become an important threshold for the access to smart buildings. The failure of inspection institutions to detect the renewal of leases may lead to the failure of intelligent systems, leading to the failure of construction equipment and causing major safety accidents such as the uncontrolled fall of construction elevators and the fall of tower crane items. As the supervisor of third-party inspection institutions, government functional departments are responsible for the failure of intelligent systems. All of them undertake the important role of intelligent building security. This paper builds an evolutionary game model with government regulatory authorities, third-party testing institutions, and intelligent construction enterprises as the three game parties, based on variables that affect the factors of the players, and discusses the possible scenarios of the stabilization strategy, which draws the following points: (1) the increase of incentives and penalties by the government is conducive to promoting the construction of high-quality intelligent buildings and the normative behavior of the third party without intention to seek rent, but the increase of incentives will not be conducive to the government fulfilling its regulatory responsibilities. (2) The reasonable reward and punishment mechanism set by the government must meet the condition that the sum of rewards and punishments for all parties is greater than their speculative returns so as to ensure the safety of intelligent buildings in the evolving and stable market environment. (3) The accountability of the superior government for the dereliction of duty of the regulatory authorities is of great significance to enhancing the stability of enterprises in building high-quality intelligent buildings. (4) It is also an effective way to avoid the construction of low-quality smart buildings by improving the listed sales income of enterprises and increasing the rent-seeking cost of enterprises. Combined with the improved SIR model, it is calculated that after the occurrence of a construction accident, when the rumor first appears, the rumor will quickly spread out of control without timely management and supervision. The conclusion of the game model provides a great reference value for the government’s regulatory behavior. The quality of the government’s regulatory behavior is directly related to the future of high-quality development of intelligent construction and also expands the application field of evolutionary game theory and SIR theory. The government should actively manage third-party testing institutions and intelligent building enterprises before construction accidents happen. After the accident, strict management and supervision should be carried out on well-known bloggers before the emergence of rumors so as to reduce the possibility of standardizing individuals’ reprinting of rumors and avoid the uncontrollable negative impact in the later period, thus seriously affecting the credibility of government supervision.