Dissolved oxygen in sea water affects marine habitats and biogeochemical cycles. Oceanic zones with oxygen deficits represent 7% of the volume and 8% of the area of the oceans, and are thought to be expanding. One of the most pronounced lies in the region off Peru, where mesoscale activity in the form of fronts and eddies is strong. Here, we study the dynamics of the Peruvian oxygen minimum zone in a Lagrangian framework, using a coupled physical-biogeochemical numerical model and finite-size Lyapunov exponent fields, to evaluate the role of mesoscale activity. We find that, at depths between 380 and 600 m, mesoscale structures have two distinct roles. First, their mean positions and paths delimit and maintain the oxygen minimum zone boundaries. Second, their high-frequency fluctuations inject oxygen across the oxygen minimum zone boundaries and eddy fluxes are one order of magnitude higher than mean oxygen fluxes. We conclude that these eddy fluxes contribute to the ventilation of the Peruvian oxygen minimum zone.