Monitoring students' engagement and understanding their learning pace in a virtual classroom becomes challenging in the absence of direct eye contact between the students and the instructor. Continuous monitoring of eye gaze and gaze gestures may produce inaccurate outcomes when the students are allowed to do productive multitasking, such as taking notes or browsing relevant content. This paper proposes Stungage - a software wrapper over existing online meeting platforms to monitor students' engagement in real-time by utilizing the facial video feeds from the students and the instructor coupled with a local on-device analysis of the presentation content. The crux of Stungage is to identify a few opportunistic moments when the students should visually focus on the presentation content if they can follow the lecture. We investigate these instances and analyze the students' visual, contextual, and cognitive presence to assess their engagement during the virtual classroom while not directly sharing the video captures of the participants and their screens over the web. Our system achieves an overall F2-score of 0.88 for detecting student engagement. Besides, we obtain 92 responses from the usability study with an average SU score of 74.18.