Following the recent success of deep neural networks (DNN) on video computer vision tasks, performing DNN inferences on videos that originate from mobile devices has gained practical significance. As such, previous approaches developed methods to offload DNN inference computations for images to cloud servers to manage the resource constraints of mobile devices. However, when it comes to video data, communicating information of every frame consumes excessive network bandwidth and renders the entire system susceptible to adverse network conditions such as congestion. Thus, in this work, we seek to exploit the temporal coherence between nearby frames of a video stream to mitigate network pressure. That is, we propose ShadowTutor, a distributed video DNN inference framework that reduces the number of network transmissions through intermittent knowledge distillation to a student model. Moreover, we update only a subset of the student's parameters, which we call partial distillation, to reduce the data size of each network transmission. Specifically, the server runs a large and general teacher model, and the mobile device only runs an extremely small but specialized student model. On sparsely selected key frames, the server partially trains the student model by targeting the teacher's response and sends the updated part to the mobile device. We investigate the effectiveness of ShadowTutor with HD video semantic segmentation. Evaluations show that network data transfer is reduced by 95% on average. Moreover, the throughput of the system is improved by over three times and shows robustness to changes in network bandwidth.