Time-staggered inhibition of EGFR, in combination with DNA damaging agents, is a useful therapeutic strategy for treating cancers, particularly drug resistant cancers such as a subset of triple-negative tumors, particularly those with high basal levels of phosphorylated EGFR. The staggered therapy was also demonstrated to be applicable to other types of tumors, especially lung cancers, which contain either high levels of phosphorylated wild-type EGFR or mutations within EGFR itself. EGFR inhibition dramatically sensitizes cancer cells to DNA damage if the drugs are given sequentially, but not simultaneously. The first drug must be administered in a dosage and for a period of time sufficient for the dynamic network rewiring of an oncogenic signature maintained by active EGFR signaling to unmask an apoptotic process that involves activation of caspase-8.