A growing interest has emerged in studying the correlation structure of spontaneous and task-induced brain activity to elucidate the functional architecture of the brain. In particular, functional networks estimated from resting state (RS) data were shown to exhibit high resemblance to those evoked by stimuli. Motivated by these findings, we propose a novel generative model that integrates RS-connectivity and stimulus-evoked responses under a unified analytical framework. Our model permits exact closed-form solutions for both the posterior activation effect estimates and the model evidence. To learn RS networks, graphical LASSO and the oracle approximating shrinkage technique are deployed. On a cohort of 65 subjects, we demonstrate increased sensitivity in fMRI activation detection using our connectivity-informed model over the standard univariate approach. Our results thus provide further evidence for the presence of an intrinsic relationship between brain activity during rest and task, the exploitation of which enables higher detection power in task-driven studies.