The article aims at selecting the most perspective mechanisms and finding the perspectives of using the integration mechanisms of education development for accelerating Russia’s economic growth. The methods of correlation and regression analysis are used. It is proved – by the example of top universities in Russia in 2020 – that the development of higher education and maximization of its contribution to the acceleration of economic growth could be achieved based on the integration mechanisms with the participation of universities. It is determined that optimization should be applied to educational (quality of higher education), scientific (R&D), and international (globalization) activities of universities, which could reach its maximum in case of an increase in the number of incubators in each university up to 5 units, number of centers of shared use of scientific equipment up to 40 units, and number of small companies up to 41. It is determined that citations and profitability (effectiveness) of universities do not depend on integration mechanisms in higher education. Such integration mechanisms as employer-sponsored education, practice bases, and technological parks do not contribute to the improvement of the indicators of universities’ activities and thus their development is inexpedient. The practical significance of the authors’ conclusions and recommendations is that they allow raising the effectiveness of university management and optimizing the organizational and managerial conditions under which the potential of universities in the sphere of support for the implementation of the social and investment model of economic growth is unlocked in the most comprehensive way.