Cancer cells with heterogeneous mutation landscapes and extensive functional redundancy easily develop resistance to monotherapies by emerging activation of compensating or bypassing pathways. To achieve more effective and sustained clinical responses, synergistic interactions of multiple druggable targets that inhibit redundant cancer survival pathways are often required. Here, we report a systematic polypharmacology strategy to predict, test, and understand the selective drug combinations for MDA-MB-231 triple-negative breast cancer cells. We started by applying our network pharmacology model to predict synergistic drug combinations. Next, by utilizing kinome-wide drug-target profiles and gene expression data, we pinpointed a synergistic target interaction between Aurora B and ZAK kinase inhibition that led to enhanced growth inhibition and cytotoxicity, as validated by combinatorial siRNA, CRISPR/Cas9, and drug combination experiments. The mechanism of such a context-specific target interaction was elucidated using a dynamic simulation of MDA-MB-231 signaling network, suggesting a cross-talk between p53 and p38 pathways. Our results demonstrate the potential of polypharmacological modeling to systematically interrogate target interactions that may lead to clinically actionable and personalized treatment options.