Investigating changes in brain function induced by mind-altering substances such as LSD is a powerful method for interrogating and understanding how mind interfaces with brain, by connecting novel psychological phenomena with their neurobiological correlates. LSD is known to increase measures of brain complexity, potentially reflecting a neurobiological correlate of the especially rich phenomenological content of psychedelic-induced experiences. Yet although the subjective stream of consciousness is a constant ebb and flow, no studies to date have investigated how LSD influences the dynamics of functional connectivity in the human brain. Focusing on the two fundamental network properties of integration and segregation, here we combined graph theory and dynamic functional connectivity from resting-state functional MRI to examine time-resolved effects of LSD on brain networks properties and subjective experiences. Our main finding is that the effects of LSD on brain function and subjective experience are non-uniform in time: LSD makes globally segregated sub-states of dynamic functional connectivity more complex, and weakens the relationship between functional and anatomical connectivity. On a regional level, LSD reduces functional connectivity of the anterior medial prefrontal cortex, specifically during states of high segregation. Time-specific effects were correlated with different aspects of subjective experiences; in particular, ego dissolution was predicted by increased small-world organisation during a state of high global integration. These results reveal a more nuanced, temporally-specific picture of altered brain connectivity and complexity under psychedelics than has previously been reported.