Cortical sensory responses are highly variable across stimulus presentations. This variability can be correlated across neurons (due to some combination of dense intracortical connectivity, cortical activity level, and cortical state), with fundamental implications for population coding. Yet the interpretation of correlated response variability (or 'noise correlation') has remained fraught with difficulty, in part because of the restriction to extracellular neuronal spike recordings. Here, we measured response variability and its correlation at the most microscopic level of electrical neural activity, the membrane potential, by obtaining dual whole-cell recordings from pairs of cortical pyramidal neurons during visual processing. We found that during visual stimulation, correlated variability adapts towards an intermediate level and that this correlation dynamic is mediated by intracortical mechanisms. A model network with external inputs, synaptic depression, and structure reproduced the observed dynamics of correlated variability. These results establish that intracortical adaptation self-organizes cortical circuits towards a balanced regime at which network coordination maintains an intermediate level.