We introduce a novel top-down end-to-end formulation of document level discourse parsing in the Rhetorical Structure Theory (RST) framework. In this formulation, we consider discourse parsing as a sequence of splitting decisions at token boundaries and use a seq2seq network to model the splitting decisions. Our framework facilitates discourse parsing from scratch without requiring discourse segmentation as a prerequisite; rather, it yields segmentation as part of the parsing process. Our unified parsing model adopts a beam search to decode the best tree structure by searching through a space of high scoring trees. With extensive experiments on the standard English RST discourse treebank, we demonstrate that our parser outperforms existing methods by a good margin in both end-to-end parsing and parsing with gold segmentation. More importantly, it does so without using any handcrafted features, making it faster and easily adaptable to new languages and domains.