Genes involved in the same function tend to have similar evolutionary histories, in that their rates of evolution covary over time. This coevolutionary signature, termed Evolutionary Rate Covariation (ERC), is calculated using only gene sequences from a set of closely related species and has demonstrated potential as a computational tool for inferring functional relationships between genes. To further define applications of ERC, we first established that roughly 55% of genetic diseases posses an ERC signature between their contributing genes. At a false discovery rate of 5% we report 40 such diseases including cancers, developmental disorders and mitochondrial diseases. Given these coevolutionary signatures between disease genes, we then assessed ERC's ability to prioritize known disease genes out of a list of unrelated candidates. We found that in the presence of an ERC signature, the true disease gene is effectively prioritized to the top 6% of candidates on average. We then apply this strategy to a melanoma-associated region on chromosome 1 and identify MCL1 as a potential causative gene. Furthermore, to gain global insight into disease mechanisms, we used ERC to predict molecular connections between 310 nominally distinct diseases. The resulting "disease map" network associates several diseases with related pathogenic mechanisms and unveils many novel relationships between clinically distinct diseases, such as between Hirschsprung's disease and melanoma. Taken together, these results demonstrate the utility of molecular evolution as a gene discovery platform and show that evolutionary signatures can be used to build informative gene-based networks.