The refinement of localization of intelligence in the human brain is converging onto a distributed network that broadly conforms to the Parieto-Frontal Integration Theory (P-FIT). While this theory has received support in the neuroimaging literature, no functional magnetic resonance imaging study to date has conducted a 18 whole-brain network-wise examination of the changes during engagement in tasks that are reliable measures of general intelligence (e.g., Raven’s Progressive Matrices Test; RPM). Seventy-nine healthy subjects were scanned while solving RPM problems and during rest. Functional networks were extracted from the RPM and resting state data using Independent Component Analysis. Twenty-nine networks were identified, 26 of which were detected in both conditions. Fourteen networks were significantly correlated with the RPM task. Fourteen networks were significantly correlated with the RPM task. The networks’ spatial maps and functional connectivity measures at 3 frequency levels (low, medium, & high) were compared between the RPM and rest conditions. The regions involved in the networks that were found to be task related were consistent with the P-FIT, localizing to the bilateral medial frontal and parietal regions, right superior frontal lobule, and the right cingulate gyrus. Functional connectivity in multiple component pairs was differentially affected across all frequency levels during the RPM task. Our findings demonstrate that functional brain networks are more stable than previously thought, and maintain their general features across resting state and engagement in a complex cognitive task. The described spatial and functional connectivity alterations that such components undergo during fluid reasoning provide a network-wise framework of the P-FIT that can be valuable for further, network based, neuroimaging inquiries regarding the neural underpinnings of intelligence.