The current positive trend in the Southern Annular Mode (SAM) is thought to reduce the growth rate of the Southern Ocean CO₂ sink because enhanced wind-driven upwelling of dissolved inorganic carbon (DIC) increases outgassing of natural CO₂. However, no study to date has quantified the potentially large role of mesoscale eddies in compensating intensified upwelling nor the mixed-layer processes in terms of their effects on CO₂ fluxes. Here we report on results from two new simulations in a regional 0.5° eddying model of the Southern Ocean. The first simulation is forced with interannually varying atmospheric reanalysis and coupled to a biogeochemistry model run under constant preindustrial atmospheric CO₂. The second simulation is like the first except that superimposed on the forcing is a poleward shifted and intensified westerlies wind anomaly consistent with the positive phase of the SAM. In response to the SAM, the Southern Ocean’s sea-to-air CO₂ flux is enhanced by 0.1 Pg C yr⁻¹ per standard deviation of the SAM, mostly from the Antarctic Zone (AZ), where enhanced surface DIC is only partly compensated by enhanced surface alkalinity. Increased mixed-layer DIC in the AZ results from a combination of increased upwelling below the mixed layer and increased vertical diffusion at the base of the mixed layer. Previous studies overlooked the latter. Thus, upward supply of DIC and alkalinity depends on associated vertical gradients just below the mixed layer, which are affected by interior ocean transport. Our eddying model study suggests that about one third of the SAM enhancement of the Ekman-induced northward DIC transport is compensated by southward transport from standing and transient eddies.