Control of cell cycle progression by stress-activated protein kinases (SAPKs) is essential for cell adaptation to extracellular stimuli. Exposure of yeast to hyperosmotic stress activates the SAPK Hog1, which delays cell cycle progression through G₁ by direct phosphorylation of the cyclin-dependent kinase (CDK) inhibitor Sic1 and by inhibition of the transcription of the genes encoding the G₁ cyclins Cln1 and 2. Additional targets of Hog1 may also play a role in this response. We used mathematical modeling and quantitative in vivo experiments to define the contributions of individual components of the G₁-S network downstream of Hog1 to this stress-induced delay in the cell cycle. The length of the arrest depended on the degree of stress and the temporal proximity of the onset of the stress to the commitment to cell division, called "Start." Hog1-induced inhibition of the transcription of the gene encoding cyclin Clb5, rather than that of the gene encoding Cln2, prevented entry into S phase upon osmostress. By controlling the accumulation of specific cyclins, Hog1 delayed bud morphogenesis (through Clns) and delayed DNA replication (through Clb5). Hog1-mediated phosphorylation and degradation of Sic1 at Start prevented residual activity of the cyclin/CDK complex Clb5/Cdc28 from initiating DNA replication before adaptation to the stress. Thus, our work defines distinct temporal roles for the actions of Hog1 on Sic1 and cyclins in mediating G₁ arrest upon hyperosmotic stress.