A fundamental goal of search engines is to identify, given a query, documents that have relevant text. This is intrinsically difficult because the query and the document may use different vocabulary, or the document may contain query words without being relevant. We investigate neural word embeddings as a source of evidence in document ranking. We train a word2vec embedding model on a large unlabelled query corpus, but in contrast to how the model is commonly used, we retain both the input and the output projections, allowing us to leverage both the embedding spaces to derive richer distributional relationships. During ranking we map the query words into the input space and the document words into the output space, and compute a query-document relevance score by aggregating the cosine similarities across all the query-document word pairs. We postulate that the proposed Dual Embedding Space Model (DESM) captures evidence on whether a document is about a query term in addition to what is modelled by traditional term-frequency based approaches. Our experiments show that the DESM can re-rank top documents returned by a commercial Web search engine, like Bing, better than a term-matching based signal like TF-IDF. However, when ranking a larger set of candidate documents, we find the embeddings-based approach is prone to false positives, retrieving documents that are only loosely related to the query. We demonstrate that this problem can be solved effectively by ranking based on a linear mixture of the DESM and the word counting features.