Rodents sleep in bouts lasting minutes; humans sleep for hours. What are the universal needs served by sleep given such variability? In sleeping mice and humans, through monitoring neural and cardiac activity (combined with assessment of arousability and overnight memory consolidation, respectively), we find a previously unrecognized hallmark of sleep that balances two fundamental yet opposing needs: to maintain sensory reactivity to the environment while promoting recovery and memory consolidation. Coordinated 0.02-Hz oscillations of the sleep spindle band, hippocampal ripple activity, and heart rate sequentially divide non-rapid eye movement (non-REM) sleep into offline phases and phases of high susceptibility to external stimulation. A noise stimulus chosen such that sleeping mice woke up or slept through at comparable rates revealed that offline periods correspond to raising, whereas fragility periods correspond to declining portions of the 0.02-Hz oscillation in spindle activity. Oscillations were present throughout non-REM sleep in mice, yet confined to light non-REM sleep (stage 2) in humans. In both species, the 0.02-Hz oscillation predominated over posterior cortex. The strength of the 0.02-Hz oscillation predicted superior memory recall after sleep in a declarative memory task in humans. These oscillations point to a conserved function of mammalian non-REM sleep that cycles between environmental alertness and internal memory processing in 20- to 25-s intervals. Perturbed 0.02-Hz oscillations may cause memory impairment and ill-timed arousals in sleep disorders.