Resting-state functional connectivity (FC) has helped reveal the intrinsic network organization of the human brain, yet its relevance to cognitive task activations has been unclear. Uncertainty remains despite evidence that resting-state FC patterns are highly similar to cognitive task activation patterns. Identifying the distributed processes that shape localized cognitive task activations may help reveal why resting-state FC is so strongly related to cognitive task activations. We found that estimating task-evoked activity flow (the spread of activation amplitudes) over resting-state FC networks allowed prediction of cognitive task activations in a large-scale neural network model. Applying this insight to empirical functional MRI data, we found that cognitive task activations can be predicted in held-out brain regions (and held-out individuals) via estimated activity flow over resting-state FC networks. This suggests that task-evoked activity flow over intrinsic networks is a large-scale mechanism explaining the relevance of resting-state FC to cognitive task activations.