Background and objectives: Non-small cell lung cancer (NSCLC) is often caused by EGFR mutations, leading to overactive cell growth pathways. Drug resistance is a significant challenge in lung cancer treatment, affecting therapy effectiveness and patient survival. However, combining drugs in research shows promise in addressing or delaying resistance, offering a more effective approach to cancer treatment. In this study, we investigated the potential alterations in the apoptotic pathway in A549 cells induced by a combined targeted therapy using tyrosine kinase inhibitors (TKIs) olmutinib and poziotinib, focusing on cell proliferation, differential gene expression, and in silico analysis of apoptotic markers. Methods: A combined targeted therapy involving olmutinib and poziotinib was investigated for its impact on the apoptotic pathway in A549 cells. Cell proliferation, quantitative differential gene expression, and in silico analysis of apoptotic markers were examined. A549 cells were treated with varying concentrations (1, 2.5, and 5 μM) of poziotinib, olmutinib, and their combination. Results: Treatment with poziotinib, olmutinib, and their combination significantly reduced cell proliferation, with the most pronounced effect at 2.5 μM (p < 0.005). A synergistic antiproliferative effect was observed with the combination of poziotinib and olmutinib (p < 0.0005). Quantitative differential gene expression showed synergistic action of the drug combination, impacting key apoptotic genes including STK-11, Bcl-2, Bax, and the Bax/Bcl-2 ratio. In silico analysis revealed direct interactions between EGFR and ERBB2 genes, accounting for 77.64% of their interactions, and 8% co-expression with downstream apoptotic genes. Molecular docking indicated strong binding of poziotinib and olmutinib to extrinsic and intrinsic apoptotic pathway markers, with binding energies of −9.4 kcal/mol and −8.5 kcal/mol, respectively, on interacting with STK-11. Conclusions: Combining poziotinib and olmutinib therapies may significantly improve drug tolerance and conquer drug resistance more effectively than using them individually in lung cancer patients, as suggested by this study’s mechanisms.