Two recent parallel research tracks link tertiary sulcal morphology sulci that emerge last in gestation and continue to develop after birth with functional features of the cerebral cortex and cognition, respectively. The first track identified a relationship between the mid fusiform sulcus (MFS) in ventral temporal cortex (VTC) and cognition in individuals with Autism Spectrum Disorder (ASD). The second track identified a new tertiary sulcus, the inframarginal sulcus (IFRMS), that serves as a tripartite landmark within the posteromedial cortex (PMC). As VTC and PMC are structurally and functionally different in individuals with ASD compared to neurotypical controls (NTs), here, we integrated these two tracks with a twofold approach. First, we tested if there are morphological differences in VTC and PMC sulci between 50 NTs and 50 individuals with ASD. Second, we tested if tertiary sulcal morphology was linked to cognition in ASD individuals. Our twofold approach replicates and extends recent findings in five ways. First, in terms of replication, the standard deviation (STD) of MFS cortical thickness (CT) was increased in ASDs compared to NTs. Second, MFS length was shorter in ASDs compared to NTs. Third, the CT STD effect extended to other VTC and PMC sulci. Fourth, a subset of VTC and PMC morphological features were correlated between regions in ASD. Fifth, IFRMS depth was negatively associated with ADOS GS score. These results empirically support a relationship between later-developing, tertiary sulci and ASD, providing a novel framework to study the relationship between brain structure and cognition in additional neurodevelopmental disorders in future studies.