In many cognitive tasks, lapses (spontaneous errors) are tacitly dismissed as the result of nuisance processes like sensorimotor noise, fatigue, or disengagement. However, some lapses could also be caused by exploratory noise: randomness in behavior that facilitates learning in changing environments. If so, then strategic processes would need only up-regulate (rather than generate) exploration to adapt to a changing environment. This view predicts that more frequent lapses should be associated with greater flexibility because these behaviors share a common cause. Here, we report that when rhesus macaques performed a set-shifting task, lapse rates were negatively correlated with perseverative error frequency across sessions, consistent with a common basis in exploration. The results could not be explained by local failures to learn. Furthermore, chronic exposure to cocaine, which is known to impair cognitive flexibility, did increase perseverative errors, but, surprisingly, also improved overall set-shifting task performance by reducing lapse rates. We reconcile these results with a state-switching model in which cocaine decreases exploration by deepening attractor basins corresponding to rule states. These results support the idea that exploratory noise contributes to lapses, affecting rule-based decision-making even when it has no strategic value, and suggest that one key mechanism for regulating exploration may be the depth of rule states.