Ensuring the high quality of online learning is one of the most significant factors in the competitiveness of universities in the educational market. The purpose of the article is to analyze the specifics of online learning for students in the context of the epidemiological crisis, to study the role of digital technologies, digital competence of teachers in improving the competitiveness of educational services. The authors used a set of methods, which included: a questionnaire survey of students of Russian universities conducted in May 2020 (N = 146 people), the focus group method (12 full-time students). A drop in the level of self-organization and self-control of students has been established, students reduce the requirements for themselves as active participants in the educational process. The conclusion is confirmed that the interest of students in online learning is connected with the teacher’s charisma, his ability to teach, while entertaining, as well as with the teacher’s active use of digital innovative technologies. The conducted research allowed us to conclude that there are a number of restrictions that limit the preservation of the quality of educational services in the context of online learning: digital inequality, insufficient development of the digital infrastructure of universities and the use of digital systems for organizing educational activities. Certain risks for maintaining the competitiveness of the university in the long term are: the inability of universities to develop high-end, comprehensive, scalable digital solutions, the request for simplification of educational work by young people due to the general availability of information materials on the Internet, high costs for updating information systems, maintaining a developed digital educational environment.