Global rankings constitute a powerful instrument for the positioning of universities in the world educational space. Institutions that are included on the list of the top five hundred get financial support from the state and from business structures; they attract the best instructors and professors from all over the world. In recognition of this, on May 7, 2012, Russian President V. V. Putin assigned the academic community the task of lifting a minimum of five universities of the Russian Federation up into the top hundred world universities by 2020. In order to achieve this goal it will be necessary to form a qualitatively new image of the future Russia by the end of the next decade. The state's policy will have to be oriented toward expanding entrepreneurship and ensuring the effectiveness of the system of state administration. Particular attention should be focused on the role played by global world rankings and their influence on the formation of a society's culture, for the purpose of achieving mutual understanding and harmony, ethnic and religious tolerance, and the stabilization of societal processes. Most of Russia's universities already have a certain ranking, image, and reputation. But the construction of rankings is seldom accorded adequate attention. One should also note some tendencies in the field of education, toward the construction of a model of interrelationships between the university, the state, business outfits, and society in the form of scientific innovative clusters, without which it is practically impossible to have a high ranking. Scientific innovative clusters that are based in universities have a number of distinctive characteristics. They must be based on the modernization of traditional sectors of the economy; they have to make it possible to turn innovations into the main vector of growth in all fields of the economy, and to form an economy of knowledge and high technologies, which becomes a key sector of the national economy. At the same time, the economy of knowledge and high technologies has to include spheres of professional education, high-technology medicine, science, communications, and so on. An analysis of the rankings of universities in parts of Russia shows how the presence of regional scientific and innovative clusters can improve the competitive positions of these institutions. It finds that clusters can act as the main breakthrough mechanism for advancing Russia's universities in world rankings on the global scale. The results obtained in the course of this study can be utilized in applications relating to universities advancement in the rankings, detailed analysis of the breakthrough mechanisms necessary to make it into the top 100 and top 200 world rankings, and also scientific developments, innovative activity, transfer of knowledge, and international cooperation.