Extracting structured data from HTML documents is a long-studied problem with a broad range of applications like augmenting knowledge bases, supporting faceted search, and providing domain-specific experiences for key verticals like shopping and movies. Previous approaches have either required a small number of examples for each target site or relied on carefully handcrafted heuristics built over visual renderings of websites. In this paper, we present a novel two-stage neural approach, named FreeDOM, which overcomes both these limitations. The first stage learns a representation for each DOM node in the page by combining both the text and markup information. The second stage captures longer range distance and semantic relatedness using a relational neural network. By combining these stages, FreeDOM is able to generalize to unseen sites after training on a small number of seed sites from that vertical without requiring expensive hand-crafted features over visual renderings of the page. Through experiments on a public dataset with 8 different verticals, we show that FreeDOM beats the previous state of the art by nearly 3.7 F1 points on average without requiring features over rendered pages or expensive hand-crafted features.