Most neurons in peripheral sensory pathways initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. It is unclear how this phenomenon affects stimulus representation in the later stages of cortical sensory processing. Here, we show that a temporally sparse and reliable stimulus representation develops naturally in a network with adapting neurons. We find that cellular adaptation plays a critical role in the transient reduction of the trial-by-trial variability of cortical spiking, providing an explanation for a wide-spread and hitherto unexplained phenomenon by a simple mechanism. In insect olfaction, cellular adaptation is sufficient to explain the emergence of the temporally sparse and reliable stimulus representation in the mushroom body, independent of inhibitory mechanisms. Our results reveal a computational principle that relates neuronal firing rate adaptation to temporal sparse coding and variability suppression in nervous systems with a sequential processing architecture.