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Individuals with autism spectrum disorder (ASD) are characterized by impairments in flexibly acquiring and maintaining new information, as well as in applying learned information for problem solving. However, the neural mechanism underpinning such impairments remains unclear. This study investigated the flexibility in the acquisition and application of visual information in ASD (aged 14–21) when they performed the Wisconsin Card Sorting Test (WCST). Behavioral data including response accuracy and latency, and prefrontal hemodynamic data measured by functional near-infrared spectroscopy (fNIRS), were collected when individuals performed WCST. Canonical general linear model and functional connectivity analyses were performed to examine the prefrontal activation and synchronization patterns, respectively. Results showed that although ASD individuals (n = 29) achieved comparable accuracy rates when compared with age- and intelligence quotient (IQ)-matched typically developing (TD; n = 26) individuals (F1,53 = 3.15, p = 0.082), ASD individuals needed significantly more time to acquire and apply WCST card sorting rules (F1,53 = 17.92, p < 0.001). Moreover, ASD individuals showed significantly lower prefrontal functional connectivity than TD individuals during WCST (F1,42 = 9.99, p = 0.003). The hypoconnectivity in ASD individuals was highly significant in the right lateral PFC in the acquisition condition (p = 0.005) and in the bilateral lateral PFC in the application condition (ps = 0.006). Furthermore, slower WCST reaction time was correlated with lower bilateral lateral PFC functional connectivity only in the application condition (ps = 0.003) but not the acquisition condition. Impairment in information acquisition and application is evident in ASD individuals and is mediated by processing speed, which is associated with lower functional connectivity in the bilateral lateral PFC when these individuals apply learned rules to solve novel problems.