The increasing frequency of major energy outages in recent years has significantly affected millions of people around the world, raising extensive concerns about enhancing infrastructure resilience to withstand and quickly recover from disasters. However, the post-disaster recovery of infrastructure functionality has been hindered by the lack of interdependency modeling of energy networks and priority identification of components, resulting in long-duration energy supply scarcity, wide-ranging service disruption, and huge social losses. Here, a skeleton-network based strategy for enhancing the resilience of integrated electricity-gas systems (IEGSs) is proposed, which can provide a clear representation of which network components should be protected and how to determine the component recovery priority considering interdependencies of power and gas systems. Using the modified energy systems in New England and Northwest China, the skeleton-network is uncovered to quickly recover more than 90% of system functionality using less than 44.3% of total resources, and consumer-affected time by energy outages decreases by more than 53%. The analysis also indicates that compared to conventional methods, the skeleton-network based strategy performs best in improving infrastructure resilience. These results elucidate the implications of skeleton-networks on quick recovery of infrastructure functionality and demonstrate resilience enhancement methods that are applicable to a wider class of coupled infrastructure networks in hazard-prone areas.