Asynchronous arrival of audiovisual information at the peripheral sensory organs is a ubiquitous property of signals in the natural environment due to differences in the propagation time of light and sound. As these cues are constantly changing their distance from the observer, rapid adaptation to asynchronies is crucial for their appropriate integration. We investigated the neural basis of rapid recalibration to asynchronous audiovisual speech in humans using a combination of psychophysics, drift diffusion modeling, and electroencephalography (EEG). Consistent with previous reports, we found that perception of audiovisual temporal synchrony depends on the temporal ordering of the previous trial. Drift diffusion modelling indicated that this recalibration effect is well accounted for by changes in the rate of evidence accumulation (i.e. drift rate). Neural responses as indexed via evoked potentials were similarly found to vary based on the temporal ordering of the previous trial. Within and across subject correlations indicated that the observed changes in drift rate and the modulation of evoked potential magnitude were related. These results indicate that the rate and direction of evidence accumulation are affected by immediate sensory history and that these changes contribute to single trial recalibration to audiovisual temporal asynchrony.