College students' motivation and engagement are regarded as essential factors to promote their academic development and wellbeing. However, motivation and engagement among college students appear to decline after they enter the university. Guided by the framework of self-determination theory, this study attempted to explore a motivational model of how three dimensions of perceived teacher support related to student motivation and class engagement, using need satisfaction as a mediator. Drew on a survey of the perceptions of 705 Chinese university students, the (...) results showed that besides structure, both autonomy support and involvement positively related to students' need satisfaction. Further, need satisfaction was positively associated with autonomous motivation, controlled motivation, and class engagement and negatively linked with amotivation. Yet, only autonomous motivation was positively predicted for class engagement. Need satisfaction and the chain from need satisfaction to autonomous motivation were found to be the significant mediators. The practical implications of educational practices are discussed. (shrink)