Despite the identification of numerous genes able to modulate lifespan, it remains unknown whether these genes interact to form a regulatory network that governs aging. Here we show that genetic interventions that extend or shorten replicative lifespan in Saccharomyces cerevisiae elicit proportional scaling of survival curve dynamics. The scalable nature of replicative lifespan distributions indicates that replicative aging is governed by a global state variable that determines cell survival by integrating effects from different risk factors. We also show that the Weibull survival function, a scale-invariant mathematical form, is capable of accurately predicting experimental survival distributions. We demonstrate that a drift-diffusion model of aging state with random challenge arrival effectively captures mortality risk. Measuring single-cell generation durations during aging, we uncover power-law dynamics with strain-specific speeds of increase in generation durations. Our application of quantitative modeling approaches to high-precision replicative aging data offers novel insights into aging dynamics and lifespan determinants in single cells.