For most of Earth's history, the ocean's interior was pervasively anoxic and showed occasional shifts in ocean redox chemistry between iron-buffered and sulfide-buffered states. These redox transitions are most often explained by large changes in external inputs, such as a strongly altered delivery of iron and sulfate to the ocean, or major shifts in marine productivity. Here, we propose that redox shifts can also arise from small perturbations that are amplified by nonlinear positive feedbacks within the internal iron and sulfur cycling of the ocean. Combining observational evidence with biogeochemical modeling, we show that both sedimentary and aquatic systems display intrinsic iron-sulfur bistability, which is tightly linked to the formation of reduced iron-sulfide minerals. The possibility of tipping points in the redox state of sediments and oceans, which allow large and nonreversible geochemical shifts to arise from relatively small changes in organic carbon input, has important implications for the interpretation of the geological rock record and the causes and consequences of major evolutionary transitions in the history of Earth's biosphere.