Evaluation of teacher behaviour from the perspective of students is beneficial to higher education institutions striving to improve student engagement. This article aims to identify and close the gaps in teacher behaviour to improve student engagement in higher education. Through a survey of 838 students in four higher education institutions in Sarawak, Malaysia, this study found that teacher behaviour had a positive and significant impact on student engagement. By empirically scrutinising students' expectations and performance evaluations of teacher behaviour, the findings revealed that significant expectation-performance gaps in teacher behaviour exist as students, across public and private universities, had expectations of teacher behaviour that were significantly higher than the actual performance of their teachers. This study demonstrated the importance of enhancing the quality of interactions and promoting interactive dialogic relationships with students in higher education to garner greater student engagement.