Chronic alcoholism is known to disrupt functions served by distributed brain systems, including limbic and frontocerebellar circuits involved in resting-state and task-activated networks subserving component processes of memory often affected in alcoholics. Using an fMRI paradigm, we investigated whether memory performance by alcoholics on a face-name association test previously observed to be problematic for alcoholics could be explained by desynchronous activity between nodes of these specific networks. While in the scanner, 18 alcoholics and 15 controls performed a face-name associative learning task with different levels of processing at encoding. This task was designed to activate the hippocampus, cerebellum, and frontal cortex. Alcoholics and controls were also scanned at rest. Twelve alcoholics and 12 controls were selected to be matched on face-name recognition performance. Task-related fMRI analysis indicated that alcoholics had preserved limbic activation but lower cerebellar activation (Crus II) than the controls in the face-name learning task. Crus II was, therefore, chosen as a seed for functional connectivity MRI analysis. At rest, the left hippocampus and left Crus II had positively synchronized activity in controls, while hippocampal and cerebellar activities were negatively synchronized in alcoholics. Task engagement resulted in hippocampal-cerebellar desynchronization in both groups. We speculate that atypical cerebello-hippocampal activity synchronization during rest in alcoholics was reset to the normal pattern of asynchrony by task engagement. Aberrations from the normal pattern of resting-state default mode synchrony could be interpreted as enabling preserved face-name associative memory in alcoholism.