Homeostatic systems that rely on genetic regulatory networks are intrinsically limited by the transcriptional response time, which may restrict a cell's ability to adapt to unanticipated environmental challenges. To bypass this limitation, cells have evolved mechanisms whereby exposure to mild stress increases their resistance to subsequent threats. However, the mechanisms responsible for such adaptive homeostasis remain largely unknown. Here, we used live-cell imaging and microfluidics to investigate the adaptive response of budding yeast to temporally controlled H 2 O 2 stress patterns. We demonstrate that acquisition of tolerance is a systems-level property resulting from nonlinearity of H 2 O 2 scavenging by peroxiredoxins and our study reveals that this regulatory scheme induces a striking hormetic effect of extracellular H 2 O 2 stress on replicative longevity. Our study thus provides a novel quantitative framework bridging the molecular architecture of a cellular homeostatic system to the emergence of nonintuitive adaptive properties.