Droughts are intensifying across the globe with potentially devastating implications for freshwater ecosystems. We used new network science approaches to investigate drought impacts on stream food webs and explored potential consequences for web robustness to future perturbations. The substructure of the webs was characterized by a core of richly connected species surrounded by poorly connected peripheral species. Although drought caused the partial collapse of the food webs, the loss of the most extinction-prone peripheral species triggered a substantial rewiring of interactions within the networks’ cores. These shifts in species interactions in the core conserved the underlying core/periphery substructure and stability of the drought-impacted webs. When we subsequently perturbed the webs by simulating species loss in silico, the rewired drought webs were as robust as the larger, undisturbed webs. Our research unearths previously unknown compensatory dynamics arising from within the core that could underpin food web stability in the face of environmental perturbations.