Monsoon precipitation is a dominant driver of floods and droughts over East Asia, which affect billions of people. The lack of air-sea coupling has been blamed for the poor East Asian monsoon precipitation simulations in atmosphere-only models because coupled models generally do better. Based on analysis of simulations from 18 pairs of atmosphere-only and coupled models from the Coupled Model Intercomparison Project phase 5, we show that the improved monsoon precipitation in coupled models is largely due to compensation from sea surface temperature (SST) biases that originate from atmosphere model biases. Such bias compensation is demonstrated using surface energy budgets and a process chain to improve both the climatological mean and interannual precipitation patterns in coupled models. Models with larger atmosphere model errors benefit more from coupling and models with smaller errors benefit less. Hence the key to simultaneously improving the simulations of East Asian monsoon precipitation and SST is a better atmosphere model.