Disconnects between science and policy, in which important scientific insights may be missed by policymakers and bad scientific advice may infect decision-making, are a long-standing concern. Yet, our systematic understanding of the use of science in policy remains limited, partly because of the difficulty in reliably tracing the coevolution of policy and science at a large, global scale. Today, the world faces a common emergency in the COVID-19 pandemic, which presents a dynamic, uncertain, yet extraordinarily consequential policy environment across the globe. We combined two large-scale databases that capture policy and science and their interactions, allowing us to examine the coevolution of policy and science during the pandemic. Our analysis suggests that many policy documents in the COVID-19 pandemic substantially access recent, peer-reviewed, and high-impact science. And policy documents that cite science are especially highly cited within the policy domain. At the same time, there is a heterogeneity in the use of science across policy-making institutions. The tendency for policy documents to cite science appears mostly concentrated within intergovernmental organizations (IGOs), such as the World Health Organization (WHO), and much less so in national governments, which consume science largely indirectly through the IGOs. This close coevolution between policy and science offers a useful indication that a key link is operating, but it has not been a sufficient condition for effectiveness in containing the pandemic.