Interdisciplinary research has emerged as a hotbed for innovation and a key approach to addressing complex societal challenges. The increasing dominance of grant-supported research in shaping scientific advances, coupled with growing interest in funding interdisciplinary work, raises fundamental questions about the effectiveness of interdisciplinary grants in fostering high-impact interdisciplinary research outcomes. Here, we quantify the interdisciplinarity of both research grants and publications, capturing 350,000 grants from 164 funding agencies across 26 countries and 1.3 million papers that acknowledged their support from 1985 to 2009. Our analysis uncovers two seemingly contradictory patterns: Interdisciplinary grants tend to produce interdisciplinary papers, which are generally associated with high impact. However, compared to disciplinary grants, interdisciplinary grants on average yield fewer papers and interdisciplinary papers they support tend to have substantially reduced impact. We demonstrate that the key to explaining this paradox lies in the power of disciplinary grants in propelling high-impact interdisciplinary research. Specifically, our results show that highly interdisciplinary papers supported by deeply disciplinary grants garner disproportionately more citations, both within their core disciplines and from broader fields. Moreover, disciplinary grants, particularly when combined with other similar grants, are more effective in producing high-impact interdisciplinary research. Amidst the rapid rise of support for interdisciplinary work across the sciences, these results highlight the hitherto unknown role of disciplinary grants in driving crucial interdisciplinary advances, suggesting that interdisciplinary research requires deep disciplinary expertise and investments.