Mathematics is one of the compulsory subjects for high school students in Indonesia. However, not many of them like mathematics. Students’ low learning engagement in mathematics is affected by the social contexts of friends, teachers, and parents and the fulfilment of the students’ basic psychological needs. Teachers’ autonomy support to improve students’ engagement is essential, especially in mathematics learning. This research was aimed at looking into the roles of the fulfilment of basic psychological needs as the element mediating teacher autonomy support and student engagement. The number of respondents of this research was 102. They were students of various high schools in Indonesia. The instruments were the autonomy support scale for measuring the teachers’ autonomy support, the “feeling I have” scale for measuring the fulfilment of basic psychological needs, and the engagement scale for measuring the students’ engagement. The employed analysis technique was the simple mediation model analysis. The results of this study indicate the partial mediation of the fulfilment of basic psychological needs between the teachers’ autonomy support and the student’s engagement. This finding implies that teachers should understand better that every student has basic psychological needs which can be fulfilled through teacher autonomy support, which, in turn, leads to learning engagement.