In response to DNA damage, the transcription factor p53 accumulates in a series of pulses. While p53 dynamics play a critical role in regulating stress responses, how p53 pulsing affects target protein expression is not well understood. Recently, we showed that p53 pulses generate diversity in target mRNA expression dynamics; however, given that mRNA and protein expression are not necessarily well correlated, it remains to be determined how p53 pulses impact target protein expression. Using computational and experimental approaches, we show that target protein decay rates filter p53 pulses: Distinct target protein expression dynamics are generated depending on the relationship between p53 pulse frequency and target mRNA and protein stability. Furthermore, by mutating the targets MDM2 and PUMA to alter their stabilities, we show that downstream pathways are sensitive to target protein decay rates. This study delineates the mechanisms by which p53 dynamics play a crucial role in orchestrating the timing of events in the DNA damage response network.