Working memory relies on the activation of both prefrontal and parietal cortex, possibly with prefrontal cortex exerting top-down control. However, there is still no mechanistic description of either capacity limitations or top-down control of maintenance of information in working memory. Here, we propose that lateral inhibition in parietal cortex limits mnemonic capacity. However, at high loads, this inhibition can be counteracted by excitatory input from prefrontal cortex, thus boosting parietal capacity. We formulate this computationally in a biophysical cortical microcircuit model, and conceptualize it in a mathematical equation. Predictions from the model were confirmed in an fMRI study. The model provides a mechanistic framework for understanding top-down control of working memory, and specifies two different contributions of prefrontal and parietal cortex to working memory capacity.