Contemporary organizations are facing the shift from Closed to Open Innovation model. The research in the area of organizational competences and skills for open innovation is needed, because the adoption of open innovation practices have brought new professional profiles and roles, leading to creation of new sets of skills and competences that managers, staff, in our case, educators and education managers, should acquire. The paper aims at answering the following research questions: what are the open innovation competence profiles within organizations? What competences shall be developed in order to obtain organizational Competence portfolio for Open Innovation? What are the challenges for education management at different levels in order to act successfully within open innovation framework? These questions are addressed drawing on the results of research carried out in the frame of the research project AISTIS. The project AISTIS aims to develop a complex methodology for the evaluation of national innovation system with reference to its evolution towards open innovation ecosystem. Mixed methods where applied for the evaluation of the macro context and organizational behaviors to support open innovation practices among the ecosystem actors. Particular role is assigned to educational organizations within the ecosystem. The research data were analyzed by using descriptive statistics, factor analysis. The insights presented in the article are part of a large-scale research that are important for researchers focused on the issues of open innovation and open social innovation management, also managers who orient innovative processes towards the open innovation paradigm, especially in educational sector.