In many documents, such as semi-structured webpages, textual semantics are augmented with additional information conveyed using visual elements including layout, font size, and color. Prior work on information extraction from semi-structured websites has required learning an extraction model specific to a given template via either manually labeled or distantly supervised data from that template. In this work, we propose a solution for "zero-shot" open-domain relation extraction from webpages with a previously unseen template, including from websites with little overlap with existing sources of knowledge for distant supervision and websites in entirely new subject verticals. Our model uses a graph neural network-based approach to build a rich representation of text fields on a webpage and the relationships between them, enabling generalization to new templates. Experiments show this approach provides a 31% F1 gain over a baseline for zero-shot extraction in a new subject vertical.