In Parkinson’s disease (PD) functional changes in the brain occur years before significant cognitive symptoms manifest yet core large-scale networks that maintain cognition and predict future cognitive decline are poorly understood. The present study investigated internetwork functional connectivity of visual (VN), anterior and posterior default mode (aDMN, pDMN), left/right frontoparietal (LFPN, RFPN), and salience (SN) networks in 63 cognitively normal PD (PDCN) and 43 healthy controls who underwent resting-state functional MRI. The functional relevance of internetwork coupling topologies was tested by their correlations with baseline cognitive performance in each group and with 2-year cognitive changes in a PDCN subsample. To disentangle heterogeneity in neurocognitive functioning, we also studied whether α-synuclein (SNCA) and microtubule-associated protein tau (MAPT) variants alter internetwork connectivity and/or accelerate cognitive decline. We found that internetwork connectivity was largely preserved in PDCN, except for reduced pDMN-RFPN/LFPN couplings, which correlated with poorer baseline global cognition. Preserved internetwork couplings also correlated with domain-specific cognition but differently for the two groups. In PDCN, stronger positive internetwork coupling topologies correlated with better cognition at baseline, suggesting a compensatory mechanism arising from less effective deployment of networks that supported cognition in healthy controls. However, stronger positive internetwork coupling topologies typically predicted greater longitudinal decline in most cognitive domains, suggesting that they were surrogate markers of neuronal vulnerability. In this regard, stronger aDMN-SN, LFPN-SN, and/or LFPN-VN connectivity predicted longitudinal decline in attention, working memory, executive functioning, and visual cognition, which is a risk factor for dementia. Coupling strengths of some internetwork topologies were altered by genetic variants. PDCN carriers of the SNCA risk allele showed amplified anticorrelations between the SN and the VN/pDMN, which supported cognition in healthy controls, but strengthened pDMN-RFPN connectivity, which maintained visual memory longitudinally. PDCN carriers of the MAPT risk allele showed greater longitudinal decline in working memory and increased VN-LFPN connectivity, which in turn predicted greater decline in visuospatial processing. Collectively, the results suggest that cognition is maintained by functional reconfiguration of large-scale internetwork communications, which are partly altered by genetic risk factors and predict future domain-specific cognitive progression.