The article aims to study the contribution of quality management in higher education through state audit and financial control to the implementation of the socio-investment model of economic growth. The article is based on the scientific hypothesis that quality management in higher education should be based on university rankings. The article presents the authors’ view on the interpretation of recent results in the research field of quality management in higher education and reveals the strengths and weaknesses of the hypothesis. Systematization and critical analysis of the indicators of quality and effectiveness in higher education based on the leading university rankings for 2022—the Ministry of Education and Science of the Russian Federation—are performed. The case study method is used for the case analysis of the management of quality and effectiveness on the example of the leading Russian university, which has been the leader of these rankings for many years: Lomonosov Moscow State University (MSU). The scientific novelty and originality of the article are associated with a systematic view of the quality and effectiveness of higher education, which was first formed by the authors through a combination and grouping of indicators from the leading university rankings for 2022. The theoretical significance of the authors’ conclusions lies in the fact that the article clearly identifies a significant contribution of the quality control of education and the performance management of universities to the implementation of the socio-investment model of economic growth. The practical significance of the obtained results is that the scientific and methodological basis for monitoring and assessing quality and effectiveness in higher education based on the leading university ratings for 2022 makes it possible to improve the state audit and financial control of university activities in the implementation of the socio-investment model of economic growth.