Despite recent progress in understanding multisensory decision-making, a conclusive mechanistic account of how the brain translates the relevant evidence into a decision is lacking. Specifically, it remains unclear whether perceptual improvements during rapid multisensory decisions are best explained by sensory (i.e., 'Early') processing benefits or post-sensory (i.e., 'Late') changes in decision dynamics. Here, we employ a well-established visual object categorisation task in which early sensory and post-sensory decision evidence can be dissociated using multivariate pattern analysis of the electroencephalogram (EEG). We capitalize on these distinct neural components to identify when and how complementary auditory information influences the encoding of decision-relevant visual evidence in a multisensory context. We show that it is primarily the post-sensory, rather than the early sensory, EEG component amplitudes that are being amplified during rapid audiovisual decision-making. Using a neurally informed drift diffusion model we demonstrate that a multisensory behavioral improvement in accuracy arises from an enhanced quality of the relevant decision evidence, as captured by the post-sensory EEG component, consistent with the emergence of multisensory evidence in higher-order brain areas.