We have evolved a robust two-component signal transduction pathway from a sensor kinase (SK) and non-partner response regulator (RR) that show weak cross-talk in vitro and no detectable cross-talk in vivo in wild-type strains. The SK, CpxA, is bifunctional, with both kinase and phosphatase activities for its partner RR. We show that by combining a small number of mutations in CpxA that individually increase phosphorylation of the non-partner RR OmpR, phosphatase activity against phospho-OmpR emerges. The resulting circuit also becomes responsive to input signal to CpxA. The effects of combining these mutations in CpxA appear to reflect complex intragenic interactions between multiple sites in the protein. However, by analyzing a simple model of two-component signaling, we show that the behavior can be explained by a monotonic change in a single parameter controlling protein-protein interaction strength. The results suggest one possible mode of evolution for two-component systems with bifunctional SKs whereby the remarkable properties and competing reactions that characterize these systems can emerge by combining mutations of the same effect.