Functional networks in the human brain give rise to complex cognitive and perceptual abilities. While the decrease of functional connectivity is linked to neurological and psychiatric disorders, less is known about the consequences of increased functional connectivity. One population that has exceptionally enhanced perceptual abilities is people with absolute pitch (AP) — an ability to categorize tones into pitch classes without reference. AP has been linked to exceptional talent as well as to psychiatric and neurological conditions. Here we show that AP possessors have increased functional activation during music listening, as well as increased degrees, clustering, and local efficiency of functional correlations, with the difference being highest around the left superior temporal gyrus. Our results provide the first evidence that increased functional connectivity in a small-world brain network is related to exceptional perceptual abilities in a healthy population.