Cells transmit information through molecular signals that often show complex dynamical patterns. The dynamic behavior of the tumor suppressor p53 varies depending on the stimulus; in response to double-strand DNA breaks, it shows a series of repeated pulses. Using a computational model, we identified a sequence of precisely timed drug additions that alter p53 pulses to instead produce a sustained p53 response. This leads to the expression of a different set of downstream genes and also alters cell fate: Cells that experience p53 pulses recover from DNA damage, whereas cells exposed to sustained p53 signaling frequently undergo senescence. Our results show that protein dynamics can be an important part of a signal, directly influencing cellular fate decisions.