The acquisition of a chemoresistant state underlies poor prognosis in many cancers, including neuroblastoma. We previously demonstrated that heterogeneity in apoptosis induction through c-Jun amino-terminal kinase (JNK) promotes a form of nongenetic chemoresistance in neuroblastoma observable at both patient and single-cell levels. As the maintenance of this JNK-impaired state in the relapse setting is a substantial barrier to the efficacy of many standard-of-care chemotherapy drugs, we combined a mechanistic, mathematical model of JNK activation with a pediatric-focused drug screen and identified approved oncology drugs capable of inducing apoptosis in a JNK-independent manner. Functional genomics further revealed that synergy between these JNK-independent drugs and standard-of-care chemotherapies emerged from differential utilization of apoptotic network components, rather than from their direct mechanistic targets. Efficacy studies with patient-derived xenograft models also confirmed that including a JNK-independent drug within existing chemotherapy backbones significantly improved response in the relapse setting, where new approaches are urgently needed.