The brain is organized into a number of large networks based on shared function, for example, high-level cognitive functions (frontoparietal network), attentional capabilities (dorsal and ventral attention networks), and internal mentation (default network). The correlations of these networks during resting-state fMRI scans varies across individuals and is an indicator of individual differences in ability. Prior work shows higher cognitive functioning (as measured by working memory and attention tasks) is associated with stronger negative correlations between frontoparietal/attention and default networks, suggesting that increased ability may depend upon the diverging activation of networks with contrasting function. However, these prior studies lack specificity with regard to the higher-level cognitive functions involved, particularly with regards to separable components of executive function (EF). Here we decompose EF into three factors from the unity/diversity model of EFs: Common EF, Shifting-specific EF, and Updating-specific EF, measuring each via factor scores derived from a battery of behavioral tasks completed by 250 adult participants (age 28) at the time of a resting-state scan. We found the hypothesized segregated pattern only for Shifting-specific EF. Specifically, after accounting for one’s general EF ability (Common EF), individuals better able to fluidly switch between task sets have a stronger negative correlation between the ventral attention network and the default network. We also report non-predicted novel findings in that individuals with higher Shifting-specific abilities exhibited more positive connectivity between frontoparietal and visual networks, while those individuals with higher Common EF exhibited increased connectivity between sensory and default networks. Overall, these results reveal a new degree of specificity with regard to connectivity/EF relationships.