Patients with neuroblastoma due to MYCN oncogene amplification and consequent N-Myc oncoprotein overexpression have very poor prognosis. The cyclin-dependent kinase 7 (CDK7)/super-enhancer inhibitor THZ1 suppresses MYCN gene transcription, reduces neuroblastoma cell proliferation, but does not cause significant cell death. The protein kinase phosphatase 1 nuclear targeting subunit (PNUTS) has recently been shown to interact with c-Myc protein and suppresses c-Myc protein degradation. Here we screened the U.S. Food and Drug Administration-Approved Oncology Drugs Set V from the National Cancer Institute, and identified tyrosine kinase inhibitors (TKIs), including ponatinib and lapatinib, as the Approved Oncology Drugs exerting the best synergistic anticancer effects with THZ1 in MYCN-amplified neuroblastoma cells. Combination therapy with THZ1 and ponatinib or lapatinib synergistically induced neuroblastoma cell apoptosis, while having little effects in normal nonmalignant cells. Differential gene expression analysis identified PNUTS as one of the genes most synergistically reduced by the combination therapy. Reverse transcription polymerase chain reaction and immunoblot analyses confirmed that THZ1 and the TKIs synergistically downregulated PNUTS mRNA and protein expression and reduced N-Myc protein but not N-Myc mRNA expression. In addition, PNUTS knockdown resulted in decreased N-Myc protein but not mRNA expression and decreased MYCN-amplified neuroblastoma cell proliferation and survival. As CDK7 inhibitors are currently under clinical evaluation in patients, our data suggest the addition of the TKI ponatinib or lapatinib in CDK7 inhibitor clinical trials in patients.