The global carbon and sulphur cycles are central to our understanding of the Earth's history, because changes in the partitioning between the reduced and oxidized reservoirs of these elements are the primary control on atmospheric oxygen concentrations. In modern marine sediments, the burial rates of reduced carbon and sulphur are positively coupled, but high-resolution isotope records indicate that these rates were inversely related during the Early Cretaceous period. This inverse relationship is difficult to reconcile with our understanding of the processes that control organic matter remineralization and pyrite burial. Here we show that the inverse correlation can be explained by the deposition of evaporites during the opening of the South Atlantic Ocean basin. Evaporite deposition can alter the chemical composition of sea water, which can in turn affect the ability of sulphate-reducing bacteria to remineralize organic matter and mediate pyrite burial. We use a reaction-transport model to quantify these effects, and the resulting changes in the burial rates of carbon and sulphur, during the Early Cretaceous period. Our results indicate that deposition of the South Atlantic evaporites removed enough sulphate from the ocean temporarily to reduce biologically mediated pyrite burial and organic matter remineralization by up to fifty per cent, thus explaining the inverse relationship between the burial rates of reduced carbon and sulphur during this interval. Furthermore, our findings suggest that the effect of changing seawater sulphate concentrations on the marine subsurface biosphere may be the key to understanding other large-scale perturbations of the global carbon and sulphur cycles.