Numerous brain lesion and fMRI studies have linked individual differences in executive abilities and fluid intelligence to brain regions of the fronto-parietal "multiple-demand" (MD) network. Yet, fMRI studies have yielded conflicting evidence as to whether better executive abilities are associated with stronger or weaker MD activations and whether this relationship is restricted to the MD network. Here, in a large-sample (n = 216) fMRI investigation, we found that stronger activity in MD regions - functionally defined in individual participants - was robustly associated with more accurate and faster responses on a spatial working memory task performed in the scanner, as well as fluid intelligence measured independently (n = 114). In line with some prior claims about a relationship between language and fluid intelligence, we also found a weak association between activity in the brain regions of the left fronto-temporal language network during an independent passive reading task, and performance on the working memory task. However, controlling for the level of MD activity abolished this relationship, whereas the MD activity-behavior association remained highly reliable after controlling for the level of activity in the language network. Finally, we demonstrate how unreliable MD activity measures, coupled with small sample sizes, could falsely lead to the opposite, negative, association that has been reported in some prior studies. Taken together, these results demonstrate that a core component of individual differences variance in executive abilities and fluid intelligence is selectively and robustly positively associated with the level of activity in the MD network, a result that aligns well with lesion studies.