This paper approaches the issue of higher entrepreneurship education in motivating young people to start their own business as a viable alternative to the successful integration of university graduates on the labour market. The fundamental question of this research is if, currently, entrepreneurship education influences students' entrepreneurial intentions and to what extent. The research results, based on the statistical analysis of data collected through a questionnaire distributed to Romanian business and engineering bachelor students in the final year, highlight that business students assessed the effectiveness of higher entrepreneurship education and its positive influence on entrepreneurial intentions to a greater extent than the engineering students. Furthermore, entrepreneurial intentions of engineering students are influenced positively much more by entrepreneurial family background than by entrepreneurship education. The findings provide important highlights for future research, in order to identify the most effective ways of approaching, modernising and expanding entrepreneurship education, aiming to increase entrepreneurial intentions among students, regardless of the graduated field of study.