We performed a mathematical analysis of functional connectivity in electroencephalography (EEG) of patients with obstructive sleep apnea (OSA) (N = 10; age: 52.8 ± 13 years; median age: 49 years; male/female ratio: 7/3), compared with a group of apparently healthy participants (N = 15; age: 51.5 ± 29.5 years; median age: 42 years; male/female ratio: 8/7), based on the calculation of wavelet bicoherence from nighttime polysomnograms. Having observed the previously known phenomenon of interhemispheric synchronization deterioration, we demonstrated a compensatory increase in intrahemispheric connectivity, as well as a slight increase in the connectivity of the central and occipital areas for high-frequency EEG activity. Significant changes in functional connectivity were extremely stable in groups of apparently healthy participants and OSA patients, maintaining the overall pattern when comparing different recording nights and various sleep stages. The maximum variability of the connectivity was observed at fast oscillatory processes during REM sleep. The possibility of observing some changes in functional connectivity of brain activity in OSA patients in a state of passive wakefulness opens up prospects for further research. Developing the methods of hypnogram evaluation that are independent of functional connectivity may be useful for implementing a medical decision support system.