In eukaryotic cells, diverse stresses trigger coalescence of RNA-binding proteins into stress granules. In vitro, stress-granule-associated proteins can demix to form liquids, hydrogels, and other assemblies lacking fixed stoichiometry. Observing these phenomena has generally required conditions far removed from physiological stresses. We show that poly(A)-binding protein (Pab1 in yeast), a defining marker of stress granules, phase separates and forms hydrogels in vitro upon exposure to physiological stress conditions. Other RNA-binding proteins depend upon low-complexity regions (LCRs) or RNA for phase separation, whereas Pab1's LCR is not required for demixing, and RNA inhibits it. Based on unique evolutionary patterns, we create LCR mutations, which systematically tune its biophysical properties and Pab1 phase separation in vitro and in vivo. Mutations that impede phase separation reduce organism fitness during prolonged stress. Poly(A)-binding protein thus acts as a physiological stress sensor, exploiting phase separation to precisely mark stress onset, a broadly generalizable mechanism.