The Fourth Industrial Revolution (4IR) is designed to challenge the old order and create a new form of social relationship and one of its tools are disruptive innovations that are designed to cause loss of employment as a result of automation that comes with disruptive technologies. In expectation of the massive retrenchment of workers, it is highly expected that youths (students) shifts away from the old belief of education for employment to self-employment. More so, an evaluation of unemployment in the country coupled with the adversities of poverty, crimes, corruption deposited into the sub-Saharan African make studying Entrepreneurial Intention (EI) cogent as the literature has affirmed that a high EI leads to enterprise creation. We, therefore, set out to determine the rate of EI amongst students of some selected universities in South-West, Nigeria and we utilized the philosophies of Theory of Planned Behaviour and Rational Choice Theory which influenced the construction of an EI Cognitive& Contextual Framework. The research design was exploratory, while the mixed method of data collection was adopted and data were generated through 403 questionnaires and 32 IDIs’ across four universities in a six-stage multi-stage sampling method. Amongst the variables that were tested, findings depicted that subjective norm is insignificantly related to EI (r=.141; β=-.049). We, therefore, recommended that for Nigeria to record internationally recognized disruptive entrepreneurial innovations, it need to significantly increase her students’ EI and create a friendly atmosphere for the easy conduction of enterprising activities for start-ups and sustain existing businesses.