Introduction: the formation of innovation-based model of the Russian economy promotes the appearance of new functions of higher education institutions’ activities aimed at sustainable development. The article analyzes various classifications of the above functions in the changed conditions of modern Russia. Materials and Methods: the authors draw on the publications by famous scientists, methods of logical analysis and synthesis, generalisation, sociological and statistical studies: a survey, expert evaluation method, documentation analysis, etc. Results: the authors’ classification of higher education institutions’ functions formed during transition to innovation-oriented model of economic development for training innovation-oriented experts is presented. The aim of new approaches is to generate innovative ideas, to transfer knowledge, to foster the skills of entrepreneurship, to ensure the competitiveness and the employability of graduates. The analysis of implementation of new functions on the example of the universities of the Penza region of the Russian Federation is made. Discussion and Conclusions: the modernisation of higher education, accompanied by update of its content and functions, involves the formation of a new national University model that reflects the specifics of modern stage of the country’s socio-economic development. Therefore changes in higher education affecting the processes of functioning of higher educational institutions are revealed. The influence of rapidly changing factors in the external and internal environment led to the formation of new and transformation of basic functions of Russian universities, the effective implementation of which will contribute to improving the quality of professional training of specialists and formation of innovative potential of new economy.