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A common thread of open-domain question answering (QA) models employs a retriever-reader pipeline that first retrieves a handful of relevant passages from Wikipedia and then peruses the passages to produce an answer. However, even state-of-the-art readers fail to capture the complex relationships between entities appearing in questions and retrieved passages, leading to answers that contradict the facts. In light of this, we propose a novel knowledge graph enhanced passage reader, namely Grape, to improve the reader performance for open-domain QA. Specifically, for each pair of question and retrieved passage, we first construct a localized bipartite graph, attributed to entity embeddings extracted from the intermediate layer of the reader model. Then, a graph neural network learns relational knowledge while fusing graph and contextual representations into the hidden states of the reader model. Experiments on three open-domain QA benchmarks show Grape can improve the state-of-the-art performance by up to 2.2 exact match score with a negligible overhead increase, with the same retriever and retrieved passages. Our code is publicly available at https://github.com/jumxglhf/GRAPE.