Cells must respond specifically to different environmental stimuli in order to survive. The signal transduction pathways involved in sensing these stimuli often share the same or homologous proteins. Despite potential cross-wiring, cells show specificity of response. We show, through modeling, that the physiological response of such pathways exposed to simultaneous and temporally ordered inputs can demonstrate system-level mechanisms by which pathways achieve specificity. We apply these results to the hyperosmolar and pheromone mitogen-activated protein (MAP) kinase pathways in the yeast Saccharomyces cerevisiae. These two pathways specifically sense osmolar and pheromone signals, despite sharing a MAPKKK, Ste11, and having homologous MAPKs (Fus3 and Hog1). We show that in a single cell, the pathways are bistable over a range of inputs, and the cell responds to only one stimulus even when exposed to both. Our results imply that these pathways achieve specificity by filtering out spurious cross-talk through mutual inhibition. The variability between cells allows for heterogeneity of the decisions.