Individuals with alcohol use disorder (AUD) manifest a variety of impairments that can be attributed to alterations in specific brain networks. The current study aims to identify features of EEG-based functional connectivity, neuropsychological performance, and impulsivity that can classify individuals with AUD (N = 30) from unaffected controls (CTL, N = 30) using random forest classification. The features included were: (i) EEG source functional connectivity (FC) of the default mode network (DMN) derived using eLORETA algorithm, (ii) neuropsychological scores from the Tower of London test (TOLT) and the visual span test (VST), and (iii) impulsivity factors from the Barratt impulsiveness scale (BIS). The random forest model achieved a classification accuracy of 80% and identified 29 FC connections (among 66 connections per frequency band), 3 neuropsychological variables from VST (total number of correctly performed trials in forward and backward sequences and average time for correct trials in forward sequence) and all four impulsivity scores (motor, non-planning, attentional, and total) as significantly contributing to classifying individuals as either AUD or CTL. Although there was a significant age difference between the groups, most of the top variables that contributed to the classification were not significantly correlated with age. The AUD group showed a predominant pattern of hyperconnectivity among 25 of 29 significant connections, indicating aberrant network functioning during resting state suggestive of neural hyperexcitability and impulsivity. Further, parahippocampal hyperconnectivity with other DMN regions was identified as a major hub region dysregulated in AUD (13 connections overall), possibly due to neural damage from chronic drinking, which may give rise to cognitive impairments, including memory deficits and blackouts. Furthermore, hypoconnectivity observed in four connections (prefrontal nodes connecting posterior right-hemispheric regions) may indicate a weaker or fractured prefrontal connectivity with other regions, which may be related to impaired higher cognitive functions. The AUD group also showed poorer memory performance on the VST task and increased impulsivity in all factors compared to controls. Features from all three domains had significant associations with one another. These results indicate that dysregulated neural connectivity across the DMN regions, especially relating to hyperconnected parahippocampal hub as well as hypoconnected prefrontal hub, may potentially represent neurophysiological biomarkers of AUD, while poor visual memory performance and heightened impulsivity may serve as cognitive-behavioral indices of AUD.