Intelligence is a fundamental ability that sets humans apart from other animal species. Despite its importance in defining human behaviour, the neural networks responsible for intelligence are not well understood. The dominant view from neuroimaging work suggests that intelligent performance on a range of tasks is underpinned by segregated interactions in a fronto-parietal network of brain regions. Here we asked whether fronto-parietal interactions associated with intelligence are ubiquitous, or emerge from more widespread associations in a task-free context. First we undertook an exploratory mapping of the existing literature on functional connectivity associated with intelligence. Next, to empirically test hypotheses derived from the exploratory mapping, we performed network analyses in a cohort of 317 unrelated participants from the Human Connectome Project. Our results revealed a novel contribution of across-network interactions between default-mode and fronto-parietal networks to individual differences in intelligence at rest. Specifically, we found that greater connectivity in the resting state was associated with higher intelligence scores. Our findings highlight the need to broaden the dominant fronto-parietal conceptualisation of intelligence to encompass more complex and context-specific network dynamics.