Sequential activity reflecting previously experienced temporal sequences is considered a hallmark of learning across cortical areas. However, it is unknown how cortical circuits avoid the converse problem: producing spurious sequences that are not reflecting sequences in their inputs. We develop methods to quantify and study sequentiality in neural responses. We show that recurrent circuit responses generally include spurious sequences, which are specifically prevented in circuits that obey two widely known features of cortical microcircuit organization: Dale's law and Hebbian connectivity. In particular, spike-timing-dependent plasticity in excitation-inhibition networks leads to an adaptive erasure of spurious sequences. We tested our theory in multielectrode recordings from the visual cortex of awake ferrets. Although responses to natural stimuli were largely non-sequential, responses to artificial stimuli initially included spurious sequences, which diminished over extended exposure. These results reveal an unexpected role for Hebbian experience-dependent plasticity and Dale's law in sensory cortical circuits.