Understanding of the neuroscientific sleep mechanisms is associated with mental/cognitive and physical well-being and pathological conditions. A prerequisite for further analysis is the identification of the sleep macroarchitecture through manual sleep staging. Several computer-based approaches have been proposed to extract time and/or frequency-domain features with accuracy ranging from 80% to 95% compared with the golden standard of manual staging. However, their acceptability by the medical community is still suboptimal. Recently, utilizing deep learning methodologies increased the research interest in computer-assisted recognition of sleep stages. Aiming to enhance the arsenal of automatic sleep staging, we propose a novel classification framework based on convolutional neural networks. These receive as input synchronizations features derived from cortical interactions within various electroencephalographic rhythms (delta, theta, alpha, and beta) for specific cortical regions which are critical for the sleep deepening. These functional connectivity metrics are then processed as multidimensional images. We also propose to augment the small portion of sleep onset (N1 stage) through the Synthetic Minority Oversampling Technique in order to deal with the great difference in its duration when compared with the remaining sleep stages. Our results (99.85%) indicate the flexibility of deep learning techniques to learn sleep-related neurophysiological patterns.