Climate models have long-standing difficulties simulating the South Pacific Convergence Zone (SPCZ) and its variability. For example, the default Zhang-McFarlane (ZM) convection scheme in the Community Atmosphere Model version 5 (CAM5) produces too much light precipitation and too little heavy precipitation in the SPCZ, with this bias toward light precipitation even more pronounced in the SPCZ than in the tropics as a whole. Here, we show that implementing a recently developed convection scheme in the CAM5 yields significant improvements in the simulated SPCZ during austral summer and discuss the reasons behind these improvements. In addition to intensifying both mean rainfall and its variability in the SPCZ, the new scheme produces a larger heavy rainfall fraction that is more consistent with observations and state-of-the-art reanalyses. This shift toward heavier, more variable rainfall increases both the magnitude and altitude of diabatic heating associated with convective precipitation, intensifying lower tropospheric convergence and increasing the influence of convection on the upper-level circulation. Increased diabatic production of potential vorticity in the upper troposphere intensifies the distortion effect exerted by convection on transient Rossby waves that pass through the SPCZ. Weaker distortion effects in simulations using the ZM scheme allow waves to propagate continuously through the region rather than dissipating locally, further reducing updrafts and weakening convection in the SPCZ. Our results outline a dynamical framework for evaluating model representations of tropical–extratropical interactions within the SPCZ and clarify why convective parameterizations that produce ‘top-heavy’ profiles of deep convective heating better represent the SPCZ and its variability.