Changes in the geological sulfur cycle are inferred from the sulfur isotopic composition of marine barite. The structure of the 34S/ 32S record from the Mesozoic to present, which includes ∼50- and 100-Ma stepwise increases, has been interpreted as the result of microbial isotope effects or abrupt changes to tectonics and associated pyrite burial. Untangling the physical processes that govern the marine sulfur cycle and associated isotopic change is critical to understanding how climate, atmospheric oxygenation, and marine ecology have coevolved over geologic time. Here we demonstrate that the sulfur outgassing associated with emplacement of large igneous provinces can produce the apparent stepwise jumps in the isotopic record when coupled to long-term changes in burial efficiency. The record of large igneous provinces map onto the required outgassing events in our model, with the two largest steps in the sulfur isotope record coinciding with the emplacement of large igneous provinces into volatile-rich sedimentary basins. This solution provides a quantitative picture of the last 120 My of change in the ocean’s largest oxidant reservoir.