Predators may alter niche overlap between prey species by eliciting divergent anti‐predator behavior. Accordingly, we exploited heterogeneous gray wolf Canis lupus presence in Washington, USA, to contrast patterns of resource and dietary overlap between mule Odocoileus hemionus and white‐tailed deer O. virginianus at sites with and without resident packs. Mule deer run (stot) in a way that is less effective as a means of fleeing from predators than the galloping gait of white‐tailed deer. Consequently, mule deer manage risk from coursing predators like wolves by avoiding encounters, whereas white‐tailed deer respond to such predators by exploiting areas where they are most likely to escape pursuit. Thus, under the ‘refuge partitioning hypothesis' whereby predators reduce prey niche overlap by eliciting use of different refugia, we predicted wolf exposure to 1) decrease resource and dietary overlap between these ungulates, and 2) induce segregation consistent with each species using different parts of the landscape to reduce their wolf risk. At the home range scale, the ways in which resource overlap diminished in the wolf areas were consistent with the prey species reducing their respective risks, particularly with respect to slope, with mule deer separating from white‐tailed deer by seeking steeper areas where wolf encounters are less likely. At the within‐home range scale, the manner in which spatial overlap decreased in relation to forest cover was consistent with species‐specific risk management, with mule deer avoiding wolf encounters by shifting toward this resource. Reduced resource overlap between the deer in areas occupied by wolves did not correspond with dietary divergence. Our findings suggest that wolf risk mediates spatial but not necessarily dietary overlap between sympatric ungulates, divergent anti‐predator behavior is a non‐consumptive pathway by which predators can reduce interspecific competition among prey, and use of disparate refugia by prey may not result in dietary divergence.