The human brain requires a continuous supply of energy to function effectively. Here, we investigated how the low-dimensional organization of intrinsic functional connectivity patterns based on resting-state functional magnetic resonance imaging relates to brain energy expenditure measured by fluorodeoxyglucose positron emission tomography. By incrementally adding more dimensions of brain organization (via functional gradients), we show that increasing amounts of variance in the map of brain energy expenditure are accounted for. Dimensions of brain organization that explained much of the variance in intrinsic brain function also accounted for a substantial share of regional variance in energy expenditure maps. This relationship was especially pronounced for maps based on the strongest connections, suggesting that weaker connections may contribute less to explaining regional energy variance. Notably, our topological model was more effective than random brain organization configurations, suggesting that brain organization may be specifically associated with energy optimization. Our results demonstrate how the spatial organization of functional connections is systematically linked to optimized energy expenditure in the human brain, providing new insights into the metabolic basis of brain function.