Despite the advances made in diagnosing and treating breast cancer, it continues to pose a significant threat to women's health. High-risk mutations can lead to high resistance to current treatments and poor prognosis. Therefore, new treatment strategies are needed. Mangiferin and silybin, two natural substances obtained from plants, have demonstrated encouraging results as anticancer drugs. This study investigated the activity of these compounds against two therapeutic targets, human epidermal growth factor receptor 2 (HER2) and epidermal growth factor receptor (EGFR). We assessed the binding affinity and stability of these compounds with the active sites of wild-type and mutated HER2 and EGFR by using computational screening techniques, namely molecular docking, density functional theory, and molecular dynamics (MD) simulations with the MMGBSA method. We used molecular docking, triplicate MD simulations summing 300 ns each, and density functional theory analysis to estimate the binding mechanism of mangiferin and silybin inside the wild-type and mutated EGFR and HER2 active regions. Moreover, an in vitro experiment showed that mangiferin and silybin inhibited the growth of two HER2-positive breast cancer cell lines, BT-474 and SK-BR-3, at micromolar concentrations. These findings suggest the potential for developing novel anticancer therapies that specifically target EGFR and HER2.