Understanding the genesis of shared trial-to-trial variability in neuronal population activity within the sensory cortex is critical to uncovering the biological basis of information processing in the brain. Shared variability is often a reflection of the structure of cortical connectivity since it likely arises, in part, from local circuit inputs. A series of experiments from segregated networks of (excitatory) pyramidal neurons in the mouse primary visual cortex challenge this view. Specifically, the across-network correlations were found to be larger than predicted given the known weak cross-network connectivity. We aim to uncover the circuit mechanisms responsible for these enhanced correlations through biologically motivated cortical circuit models. Our central finding is that coupling each excitatory subpopulation with a specific inhibitory subpopulation provides the most robust network-intrinsic solution in shaping these enhanced correlations. This result argues for the existence of excitatory–inhibitory functional assemblies in early sensory areas which mirror not just response properties but also connectivity between pyramidal cells. Furthermore, our findings provide theoretical support for recent experimental observations showing that cortical inhibition forms structural and functional subnetworks with excitatory cells, in contrast to the classical view that inhibition is a nonspecific blanket suppression of local excitation.