Preterm birth is the greatest risk factor for lifelong neurocognitive deficits, globally. The effect of prematurity on early cortical network function has, however, remained poorly understood. Here, we developed a novel methodology that allows reliable assessment of functional connectivity in neonatal brain activity at millisecond and multisecond scales in terms of cortical phase and amplitude correlations, respectively. We measured scalp electroencephalography at term-equivalent age in infants exposed to very early prematurity as well as in healthy controls. We found that newborn cortical activity organizes into multiplex networks that differ significantly between vigilance states. As compared with healthy control infants, prematurity was found to cause frequency-specific patterns of dysconnectivity in cortical network, changes that were distinct for networks of phase and amplitude correlations. Neuroanatomically, the most prominent markers of prematurity were found in connections involving the frontal regions. Phase synchrony in frontally connected networks was correlated with newborn neurological performance, suggesting the first measure of cortical functional coupling that correlates with neurological performance in human infant.