South Asian monsoon depressions are convectively coupled cyclonic vortices that form and intensify in a region of easterly vertical shear of the horizontal wind. Observations of maximum precipitation down-shear of the cyclonic center have led to prior theories of quasi-geostrophic (QG) control of moist convection in these storms, and this study examines the interaction between adiabatic QG lifting and moist convection in monsoon depressions using an atmospheric reanalysis and idealized model. Inversion of the QG omega equation in the reanalysis shows that, in the down-shear, heavily precipitating region, adiabatic QG ascent, due to advection of vorticity and temperature, is comparable to diabatic ascent in the lower troposphere, while diabatic ascent dominates in the middle and upper troposphere. The causal influence of adiabatic QG lifting on precipitating ascent in monsoon depressions is then examined in the Column-QG modeling framework, where moist convection evolves in the presence of vorticity and temperature advection. The heavy observed precipitation rates are only simulated when moist convective heating amplifies QG ascent, with this interaction accounting for roughly 40 percent of the increase in precipitation relative to the basic state. Another 40 percent of this increase is produced by enhanced surface wind speed in the surface enthalpy flux parameterization, which represents the effect of cyclonic winds in the monsoon depression. Horizontal advection of the mean-state poleward moisture gradient accounts for the remaining 20 percent of the precipitation increase. In the up-shear region, adiabatic QG subsidence and horizontal moisture advection both suppress precipitation, and are opposed by wind-enhanced surface enthalpy fluxes.