The cycles of carbon and oxygen at the Earth surface are intimately linked, where the burial of organic carbon into sediments represents a source of oxygen to the surface environment. This coupling is typically quantified through the isotope records of organic and inorganic carbon. Yet, the late Neoproterozoic Eon, the time when animals first evolved, experienced wild isotope fluctuations which do not conform to our normal understanding of the carbon cycle and carbon-oxygen coupling. We interpret these fluctuations with a new carbon cycle model and demonstrate that all of the main features of the carbonate and organic carbon isotope record can be explained by the release of methane hydrates from an anoxic dissolved organic carbon-rich ocean into an atmosphere containing oxygen levels considerably less than today.