Genetically identical cells can respond heterogeneously to cancer therapy, with a subpopulation of cells often entering a temporarily arrested treatment-tolerant state before repopulating the tumor. To investigate how heterogeneity in the cell cycle arrest protein p21 arises, we imaged the dynamics of p21 transcription and protein expression along with those of p53, its transcriptional regulator, in single cells using live cell fluorescence microscopy. Surprisingly, we found that the rate of p21 transcription depends on the change in p53 rather than its absolute level. Through combined theoretical and experimental modeling, we determined that p21 transcription is governed by an incoherent feedforward loop mediated by MDM2. This network architecture facilitates rapid induction of p21 expression and variability in p21 transcription. Abrogating the feedforward loop overcomes rapid S-phase p21 degradation, with cells transitioning into a quiescent state that transcriptionally resembles a treatment-tolerant persister state. Our findings have important implications for therapeutic strategies based on activating p53.