The article aims to develop recommendations for improving universities' innovation management, their financial regulation and influence on the pedagogical process. The authors examined the essence of innovation and innovation in the education system, clearly presented their classification and methods of modernization, analyzed modern problems of management and financing of innovation in education. The authors contributed to managing innovation processes in the education system and improved the generalized model of the innovation process in the education system. As an improvement in the foundations of innovation management, the authors proposed the joint influence of the laws of the course of innovation processes, principles, stages, and functions of innovative processes that determine the direction of management activities at all stages. To improve financing by innovation, the authors empirically determined which tools are the most effective and efficient. The authors used the methods of expert assessments to present their proposals visually. At the same time, the authors emphasize the importance of using the synergistic effect here, too. The rest of the instruments will only enhance the effectiveness of the priority instrument for financing innovations in the education system. The systematic use of other tools is no less compelling. The proposed ways of improvement will allow universities to manage innovations and their financing more effectively.