While there has been substantial progress in factoid question-answering (QA), answering complex questions remains challenging, typically requiring both a large body of knowledge and inference techniques. Open Information Extraction (Open IE) provides a way to generate semi-structured knowledge for QA, but to date such knowledge has only been used to answer simple questions with retrieval-based methods. We overcome this limitation by presenting a method for reasoning with Open IE knowledge, allowing more complex questions to be handled. Using a recently proposed support graph optimization framework for QA, we develop a new inference model for Open IE, in particular one that can work effectively with multiple short facts, noise, and the relational structure of tuples. Our model significantly outperforms a state-of-the-art structured solver on complex questions of varying difficulty, while also removing the reliance on manually curated knowledge.