Previous research has underscored the negative effects on students of the abrupt shift to online delivery of education due to the COVID-19 pandemic. Positive education applies the principles of positive psychology to education, which highlights the importance of students' well-being and fosters holistic development. This study investigated whether students' well-being at the start of the semester can predict their academic engagement mid-way through the semester. We collected data on students' well-being and academic engagement in two waves; first, at the beginning of the semester (Time 1) and then 3 months in the semester (Time 2). We tested the students' general well-being and the positive emotion, engagement, relationships, meaning, accomplishment (PERMA) elements at Time 1 with their academic engagement in terms of behavioral, emotional, and cognitive facets at Time 2. Our results show that general well-being at Time positively predicts their total academic engagement and all engagement facets. However, among the PERMA elements, the Meaning element is not correlated with students' engagement or any of its facets. We also tested whether there was a significant change in student well-being and engagement from the start of the semester and midway through. We found that there is a significant small increase in well-being and engagement. Our findings suggest the importance of well-being as a potentially positive resource for students where students with better well-being tend to be more academically engaged. Educational institutions may consider fostering student well-being in their goals to improve the academic success of students.