Hemispheric lateralization is linked to potential cognitive advantages. It is considered a driving force behind the generation of human intelligence. However, establishing quantitative links between the degree of lateralization and intelligence in humans remains elusive. In this study, we propose a novel framework that utilizes the hyperaligned multidimensional representation space derived from hemispheric functional gradients to compute between-hemisphere distances within this space. Our analysis improves the functional alignment between the hemispheres, making it possible to delineate aspects of human brain lateralization that relate to individual differences in cognitive ability more precisely. Applying this framework to the Human Connectome Project (HCP) large cohort (N = 777) identified the highest functional divergence within the frontoparietal control network across the two hemispheres. We found that spatial variability in between-hemisphere functional divergence aligned with the lateralized response patterns across multiple tasks, cortical myelination and evolutionary expansion. Furthermore, both global divergence between the cerebral hemispheres and regional divergence within the multiple demand network were positively associated with fluid composite score and partially mediated the influence of brain size on individual differences in fluid intelligence. Together, these findings illuminate the profound significance of brain lateralization as a fundamental organizational principle of the human brain, providing direct evidence that hemispheric lateralization supports human fluid intelligence.Significance StatementA novel framework is developed to estimate between-hemisphere distance in a functional representation space derived from connectivity gradients. This framework is used in a large sample to delineate functional lateralization in humans. Our findings offer direct proof that a larger functional difference between the two hemispheres is associated with better fluid intelligence, indicating that functional lateralization is the optimal organization for cognitive processing. Importantly, our findings reveal that the functional distance between the left and right hemispheres partially mediates the impact of brain size on fluid intelligence.