There is an unmet medical need for the development of new targeted therapeutic strategies for triple-negative breast cancer (TNBC). With drug combination screenings, we found that the triple combination of the protein kinase inhibitors (PKIs) of the epidermal growth factor receptor (EGFR), v-akt murine thymoma viral oncogene homolog (AKT), and MAPK/ERK kinase (MEK) is effective in inducing apoptosis in TNBC cells. A set of PKIs were first screened in combination with gefitinib in the TNBC cell line, MDA-MB-231. The AKT inhibitor, AT7867, was identified and further analyzed in two mesenchymal stem-like (MSL) subtype TNBC cells, MDA-MB-231 and HS578T. A combination of gefitinib and AT7867 reduced the proliferation and long-term survival of MSL TNBC cells. However, gefitinib and AT7867 induced the activation of the rat sarcoma (RAS)/ v-raf-1 murine leukemia viral oncogene homolog (RAF)/MEK/ extracellular signal-regulated kinase (ERK) pathway. To inhibit this pathway, MEK/ERK inhibitors were further screened in MDA-MB-231 cells in the presence of gefitinib and AT7867. As a result, we identified that the MEK inhibitor, PD-0325901, further enhanced the anti-proliferative and anti-clonogenic effects of gefitinib and AT7867 by inducing apoptosis. Our results suggest that the dual inhibition of the AKT and MEK pathways is a novel potential therapeutic strategy for targeting EGFR in TNBC cells.