Molecular targeted drugs are clinically effective anti-cancer therapies. However, tumours treated with single agents usually develop resistance. Here we use colorectal cancer (CRC) as a model to study how the acquisition of resistance to EGFR-targeted therapies can be restrained. Pathway-oriented genetic screens reveal that CRC cells escape from EGFR blockade by downstream activation of RAS-MEK signalling. Following treatment of CRC cells with anti-EGFR, anti-MEK or the combination of the two drugs, we find that EGFR blockade alone triggers acquired resistance in weeks, while combinatorial treatment does not induce resistance. In patient-derived xenografts, EGFR-MEK combination prevents the development of resistance. We employ mathematical modelling to provide a quantitative understanding of the dynamics of response and resistance to these single and combination therapies. Mechanistically, we find that the EGFR-MEK Combo blockade triggers Bcl-2 and Mcl-1 downregulation and initiates apoptosis. These results provide the rationale for clinical trials aimed at preventing rather than intercepting resistance.