E-learning significantly broadens the scope for students to participate in extracurricular self-directed learning to achieve personal goals. However, the existing research has somewhat overlooked this particular setting. Our study delves into how self-determination theory shapes student engagement in learning, influenced by social support, flow experience, and self-regulated learning, while also examining the mediating role of self-determination theory. We gathered 593 questionnaires from students across various disciplines and levels of learning in five Chinese universities. Through structural equation model, we tested 13 hypotheses and several mediating effects basing on self-determination theory. Our findings revealed that social support can predict relatedness, while both flow experience and self-regulated learning have significant impacts on the three basic psychological needs. Furthermore, we observed that competence and relatedness have impacts on the motivation of self-determination theory. A significant positive association exists between motivation and student learning engagement, and insignificant direct pathways have no indirect effect on mediating effects. We discussed the similarities and differences between out-of-class self-directed e-learning and traditional in-class e-learning, considering the same influencing factors. We also offered constructive insights for students to effectively reaching their personal goals.