Recent action recognition models have achieved impressive results by integrating objects, their locations and interactions. However, obtaining dense structured annotations for each frame is tedious and time-consuming, making these methods expensive to train and less scalable. At the same time, if a small set of annotated images is available, either within or outside the domain of interest, how could we leverage these for a video downstream task? We propose a learning framework StructureViT (SViT for short), which demonstrates how utilizing the structure of a small number of images only available during training can improve a video model. SViT relies on two key insights. First, as both images and videos contain structured information, we enrich a transformer model with a set of object tokens that can be used across images and videos. Second, the scene representations of individual frames in video should ``align'' with those of still images. This is achieved via a Frame-Clip Consistency loss, which ensures the flow of structured information between images and videos. We explore a particular instantiation of scene structure, namely a Hand-Object Graph, consisting of hands and objects with their locations as nodes, and physical relations of contact/no-contact as edges. SViT shows strong performance improvements on multiple video understanding tasks and datasets, including the first place in the Ego4D CVPR'22 Point of No Return Temporal Localization Challenge.