The EGF receptor (EGFR) is therapeutically targeted by antibodies and small molecules in solid tumors including lung, colorectal, and breast cancer. However, chemotherapy remains important, and efforts to improve efficacy through combination with targeted agents is challenging. This study examined the effects of short and long durations of exposure to the EGFR- and HER2-targeted tyrosine kinase inhibitors (TKI) gefitinib and lapatinib, on induction of cell death and DNA damage by topoisomerase IIα (Topo IIα) poisons, in the SK-Br-3 HER2-amplified breast cancer cell line. Short exposure to either gefitinib or lapatinib for 1 hour did not affect the induction of apoptosis by the Topo IIα poisons doxorubicin, etoposide, and m-AMSA. In contrast, cells treated for 48 hours were resistant to all three drugs. Short exposure (1 hour) to TKI did not alter the number of DNA single- or double-strand breaks (DSB) induced, whereas longer exposure (48 hours) reduced the number of DNA DSBs and the formation of γ-H2AX foci. Both gefitinib and lapatinib reduced the expression and activity of Topo IIα at 48 hours. Studies using a cell line with inducible downregulation of Topo IIα showed that expression of Topo IIα, and not Topo IIβ, determined the number of DNA strand breaks induced by these chemotherapeutic agents. These results indicate that prolonged exposure to TKIs targeting EGFR and HER2 induce resistance to doxorubicin, etoposide, and m-AMSA through downregulation of Topo IIα. This may explain why their addition to chemotherapy regimens have not increased efficacy.