Recent behavioral investigations have revealed that autistics perform more proficiently on Raven's Standard Progressive Matrices (RSPM) than would be predicted by their Wechsler intelligence scores. A widely-used test of fluid reasoning and intelligence, the RSPM assays abilities to flexibly infer rules, manage goal hierarchies, and perform high-level abstractions. The neural substrates for these abilities are known to encompass a large frontoparietal network, with different processing models placing variable emphasis on the specific roles of the prefrontal or posterior regions. We used functional magnetic resonance imaging to explore the neural bases of autistics' RSPM problem solving. Fifteen autistic and eighteen non-autistic participants, matched on age, sex, manual preference and Wechsler IQ, completed 60 self-paced randomly-ordered RSPM items along with a visually similar 60-item pattern matching comparison task. Accuracy and response times did not differ between groups in the pattern matching task. In the RSPM task, autistics performed with similar accuracy, but with shorter response times, compared to their non-autistic controls. In both the entire sample and a subsample of participants additionally matched on RSPM performance to control for potential response time confounds, neural activity was similar in both groups for the pattern matching task. However, for the RSPM task, autistics displayed relatively increased task-related activity in extrastriate areas (BA18), and decreased activity in the lateral prefrontal cortex (BA9) and the medial posterior parietal cortex (BA7). Visual processing mechanisms may therefore play a more prominent role in reasoning in autistics.