Cancer treatment decisions are increasingly guided by which specific genes are mutated within each patient’s tumor. For example, agents inhibiting the epidermal growth factor receptor (EGFR) benefit many colorectal cancer (CRC) patients, with the general exception of those whose tumor includes a KRAS mutation. However, among the various KRAS mutations, the G13D mutation behaves differently; for unknown reasons, CRC patients with the KRAS G13D mutation (also written KRASG13D) appear to benefit from the EGFR-blocking antibody cetuximab. Controversy surrounds this observation, because it appears to contradict the well-established mechanisms of EGFR signaling and of RAS mutations. Here, we identified a systems-level, mechanistic basis that explains why KRASG13D cancers respond to EGFR inhibition. We first investigated the problem with a computational model of RAS signaling, which unexpectedly revealed that the known biophysical differences between the three most common KRAS mutant proteins are sufficient to generate different sensitivities to inhibition. Computation and experimentation together revealed a non-intuitive, mutant-specific dependency of wild-type RAS activation by EGFR that is determined by the interaction strength between KRAS and the tumor suppressor neurofibromin (NF1). KRAS mutants that strongly interact with NF1 drive wild-type RAS activation in an EGFR independent manner through competitive inhibition of NF1, whereas KRAS G13D cells remain dependent upon EGFR for wild-type Ras activation because they cannot competitively inhibit NF1 due to a weak interaction between these two proteins. Overall, our work demonstrates how systems approaches enable mechanism-based inference in genomic medicine and can help identify patients for selective therapeutic strategies.