The brain uses context and prior knowledge to repair degraded sensory inputs and improve perception. For example, listeners hear speech continuing uninterrupted through brief noises, even if the speech signal is artificially removed from the noisy epochs. In a functional MRI study, we show that this temporal filling-in process is based on two dissociable neural mechanisms: the subjective experience of illusory continuity, and the sensory repair mechanisms that support it. Areas mediating illusory continuity include the left posterior angular gyrus (AG) and superior temporal sulcus (STS) and the right STS. Unconscious sensory repair occurs in Broca's area, bilateral anterior insula, and pre-supplementary motor area. The left AG/STS and all the repair regions show evidence for word-level template matching and communicate more when fewer acoustic cues are available. These results support a two-path process where the brain creates coherent perceptual objects by applying prior knowledge and filling-in corrupted sensory information.