Functional connectivity (FC) is the most popular method for recovering functional networks of brain areas with fMRI. However, because FC is defined as temporal correlations in brain activity, FC networks are confounded by noise and lack a precise functional role. To overcome these limitations, we developed model connectivity (MC). MC is defined as similarities in encoding model weights, which quantify reliable functional activity in terms of interpretable stimulus- or task-related features. To compare FC and MC, both methods were applied to a naturalistic story listening dataset. FC recovered spatially broad networks that are confounded by noise, and that lack a clear role during natural language comprehension. By contrast, MC recovered spatially localized networks that are robust to noise, and that represent distinct categories of semantic concepts. Thus, MC is a powerful data-driven approach for recovering and interpreting the functional networks that support complex cognitive processes.