The relevance of the problem under study is conditioned by the socially important need of the contemporary university education to train highly qualified personnel in all directions of activity, to form and develop a professional person of a high intellectual, moral and spiritual culture. The objective of the paper consists in giving theoretical grounds for the significant aspects of pedagogical implementation of training technologies and methods that are associated with the humanitarian vectors of generating the personal, "living" knowledge in the course of epistemic transformation of the content-related and essential parameters of interaction between subjects of the educational process at higher school. The leading approach to studying this problem was the activity-based one. It is consistently implemented in the competency-based paradigm of the contemporary higher education and it implies the epistemologically centered transformation of the pedagogical functions range of a university teacher. This would become a qualitative foundation for the new level of organizing the project, creative, scientific and research activities of students within the problem-solving and reflexive discourse of working within the group and interactive communication. In particular, in the contemporary university education paradigm, the epistemological interaction of teachers and students is to be the fact of the creative availability of intellectual relationships in the co-being reality of gaining the personally important, "living" knowledge. It acts as a factor of productive performance for the project-oriented epistemic technologies of forming a professional person of a high intellectual and spiritual culture. So it implies a generalized ability of a teacher to mentally activate the motivation and need sphere of the learners' personality pushing it towards intellectual openness to new knowledge and towards sensible responsible actions in the constructive context of project image of being. The materials of the paper can be of use for higher school teachers who are actual and effective participants in the innovation process of cognitive transformation that the contemporary university's mission undergoes, it being implemented within the epistemological paradigm "education through scientific research, heuristic cooperation and creative discoveries".