Prominent applications of sentiment analysis are countless, including areas such as marketing, customer service and communication. The conventional bag-of-words approach for measuring sentiment merely counts term frequencies; however, it neglects the position of the terms within the discourse. As a remedy, we thus develop a discourse-aware method that builds upon the discourse structure of documents. For this purpose, we utilize rhetorical structure theory to label (sub-)clauses according to their hierarchical relationships and then assign polarity scores to individual leaves. To learn from the resulting rhetoric structure, we propose a tensor-based, tree-structured deep neural network (named RST-LSTM) in order to process the complete discourse tree. The underlying attention mechanism infers the salient passages of narrative materials. In addition, we suggest two algorithms for data augmentation (node reordering and artificial leaf insertion) that increase our training set and reduce overfitting. Our benchmarks demonstrate the superior performance of our approach. Ultimately, this work advances the status quo in natural language processing by developing algorithms that incorporate semantic information.