The Neoproterozoic era witnessed a succession of biological innovations that culminated in diverse animal body plans and behaviours during the Ediacaran-Cambrian radiations. Intriguingly, this interval is also marked by perturbations to the global carbon cycle, as evidenced by extreme fluctuations in climate and carbon isotopes. The Neoproterozoic isotope record has defied parsimonious explanation because sustained C-12-enrichment (low delta C-13) in seawater seems to imply that substantially more oxygen was consumed by organic carbon oxidation than could possibly have been available. We propose a solution to this problem, in which carbon and oxygen cycles can maintain dynamic equilibrium during negative delta C-13 excursions when surplus oxidant is generated through bacterial reduction of sulfate that originates from evaporite weathering. Coupling of evaporite dissolution with pyrite burial drives a positive feedback loop whereby net oxidation of marine organic carbon can sustain greenhouse forcing of chemical weathering, nutrient input and ocean margin euxinia. Our proposed framework is particularly applicable to the late Ediacaran 'Shuram' isotope excursion that directly preceded the emergence of energetic metazoan metabolisms during the Ediacaran-Cambrian transition. Here we show that non-steady-state sulfate dynamics contributed to climate change, episodic ocean oxygenation and opportunistic radiations of aerobic life during the Neoproterozoic era.