This study investigates how autonomy, competence, and relatedness needs impact student engagement during work placement learning tasks (student engagement henceforth), mediated by intrinsic motivation-to-know, and moderated by perceived instructor autonomy support. Conducted with 311 undergraduate students across 116 Nigerian firms/organizations, our analysis utilized a cross-lagged panel approach. We found positive associations between autonomy, competence, relatedness, and student engagement. Additionally, intrinsic motivation-to-know mediated the relationships between these needs and student engagement. Perceived autonomy support moderated both direct and indirect effects of competence and relatedness on engagement via intrinsic motivation-to-know, across varying levels. These findings have significant implications for both theory and practice.