Understanding neural network dysfunction in neurodegenerative disease is imperative to effectively develop network-modulating therapies. In Alzheimer's disease (AD), cognitive decline associates with deficits in resting-state functional connectivity of diffuse brain networks. The goal of the current study was to test whether specific cognitive impairments in AD spectrum correlate with reduced functional connectivity of distinct brain regions. We recorded resting-state functional connectivity of alpha-band activity in 27 patients with AD spectrum--22 patients with probable AD (5 logopenic variant primary progressive aphasia, 7 posterior cortical atrophy, and 10 early-onset amnestic/dysexecutive AD) and 5 patients with mild cognitive impairment due to AD. We used magnetoencephalographic imaging (MEGI) to perform an unbiased search for regions where patterns of functional connectivity correlated with disease severity and cognitive performance. Functional connectivity measured the strength of coherence between a given region and the rest of the brain. Decreased neural connectivity of multiple brain regions including the right posterior perisylvian region and left middle frontal cortex correlated with a higher degree of disease severity. Deficits in executive control and episodic memory correlated with reduced functional connectivity of the left frontal cortex, whereas visuospatial impairments correlated with reduced functional connectivity of the left inferior parietal cortex. Our findings indicate that reductions in region-specific alpha-band resting-state functional connectivity are strongly correlated with, and might contribute to, specific cognitive deficits in AD spectrum. In the future, MEGI functional connectivity could be an important biomarker to map and follow defective networks in the early stages of AD.