A salient neuroanatomical feature of the human brain is its pronounced cortical folding, and there is mounting evidence that sulcal morphology is relevant to functional brain architecture and cognition. Recent studies have emphasized putative tertiary sulci (pTS): small, shallow, late-developing, and evolutionarily new sulci that have been posited to serve as functional landmarks in association cortices. A fruitful approach to characterizing brain architecture has been to delineate regions based on transitions in fMRI-based functional connectivity profiles; however, exact regional boundaries can change depending on the data used to generate the parcellation. As sulci are fixed neuroanatomical structures, here, we propose to anchor functional connectivity to individual-level sulcal anatomy. We characterized fine-grained patterns of functional connectivity across 42 sulci in lateral prefrontal (LPFC) and lateral parietal cortices (LPC) in a pediatric sample (N = 43; 20 female; ages 7-18). Further, we test for relationships between pTS morphology and functional network architecture, focusing on depth as a defining characteristic of these shallow sulci, and one that has been linked to variability in cognition. We find that 1) individual sulci have distinct patterns of connectivity, but nonetheless cluster together into groups with similar patterns — in some cases with distant rather than neighboring sulci, 2) there is moderate agreement in cluster assignments at the group and individual levels, underscoring the need for individual-level analyses, and 3) across individuals, greater depth was associated with higher network centrality for several pTS. These results highlight the importance of considering individual sulcal morphology for understanding functional brain organization.