Identification of genes whose basal mRNA expression can predict the sensitivity of tumor cells to treatments can play an important role in individualized cancer medicine. Screening the expression of these genes in the tumor tissue may suggest the best course of chemotherapy or suggest a combination of drugs to overcome chemoresistance. In this study, we developed a computational method called Prioritization of Genes Enhanced with Network Information (ProGENI), to identify such genes by leveraging their basal expressions and prior knowledge in the form of protein-protein and genetic interactions. ProGENI is based on identifying a small set of genes where a combination of their expression and the activity level of the network module surrounding them shows a high correlation with drug response, followed by the ranking of the genes based on their relevance to this set using random walk techniques. Our analysis on two relatively new and large datasets of cell lines and their response to a large compendium of drugs revealed a significant improvement in predicting drug sensitivity using ProGENI compared to methods that do not consider network information. In addition, we used literature evidence and siRNA knockdown experiments to confirm the effect of highly ranked genes on the sensitivity of three chemotherapy drugs: cisplatin, docetaxel and doxorubicin. Our results confirmed the role of 73% of the genes (33 out of 45) identified using ProGENI in the sensitivity of cell lines to these drugs. These results suggest ProGENI to be a powerful computational technique in identifying genes determining the drug response.