Synthetic lethality is a genetic interaction wherein two otherwise nonessential genes cause cellular inviability when knocked out simultaneously. Drugs can mimic genetic knock-out effects, therefore, our understanding of promiscuous drugs, polypharmacology-related adverse drug reactions, and multi-drug therapies, especially cancer combination therapy, may be informed by a deeper understanding of synthetic lethality. However, the colossal experimental burden in humans necessitates in silico methods to guide the identification of synthetic lethal pairs. Here, we present SINaTRA (Species-INdependent TRAnslation), a network-based methodology that discovers genome-wide synthetic lethality in translation between species. SINaTRA uses connectivity homology, defined as biological connectivity patterns that persist across species, to identify synthetic lethal pairs. Importantly, our approach does not rely on genetic homology or structural and functional similarity, and it significantly outperforms models utilizing these data. We validate SINaTRA by predicting synthetic lethality in S. pombe using S. cerevisiae data, then identify over one million putative human synthetic lethal pairs to guide experimental approaches. We highlight the translational applications of our algorithm for drug discovery by identifying clusters of genes significantly enriched for single- and multi-drug cancer therapies. 