Among mechanisms accounting for atmospheric pCO2 drawdown during glacial periods, processes operating in the North Atlantic (NA) and Southern Ocean (SO) have been proposed to be critical. Their individual and synergic effects during a course of glaciation, however, remain enigmatic. We conducted simulations to examine these effects at idealized glacial stages. Under early-glacial-like conditions, cooling in the SO can trigger an initial pCO2 drawdown while the associated sea ice expansion has little impact on air-sea gas exchange. Under later glacial-like conditions, further cooling in the NA enhances ocean carbon uptake due to a stronger solubility pump, and the SO-induced stronger deep stratification prevents carbon exchange between the deep and upper ocean. Meanwhile, strengthened dust deposition increases the SO contribution to the global biological pump, and CO2 outgassing is suppressed by fully extended sea ice cover. More carbon is then stored in the deep Pacific, acting as a passive reservoir.