Human disturbance has the potential to alter competitive interactions, favoring species better able to adapt to areas used by humans. One such species is the spotted hyena (Crocuta crocuta), which has been successful in human-dominated areas throughout Africa. In addition, hyenas are frequently successful in kleptoparasiting prey brought down by other carnivore species (e.g., leopards [Panthera pardus]). In the Udzungwa Mountains of Tanzania, leopard density declines sharply close to human settlements, and hyenas are their only competitors. Using camera trap data and a spatio-temporal occupancy model, we assessed the relative dominance of each species through spatial co-occurrence, altered activity patterns and temporary site avoidance. We tested the hypothesis that hyenas gain a competitive advantage over leopards in human-dominated areas due to their relatively higher tolerance for anthropogenic activities. We found that while hyena occupancy was best predicted by prey occupancy and not strongly affected by landscape factors associated with humans, leopards, especially male leopards, were less likely to be detected close to human settlements. Female leopards, which are smaller than males, exhibited activity shifts and temporary site avoidance in response to hyenas. In response to male leopards, hyenas shifted their activity patterns to become more active around dusk and dawn. These results suggest that while hyenas may be behaviorally dominant over female leopards, they are subordinate to male leopards. We found that male leopards and hyenas were less likely to co-occur closer to people, especially where prey was scarce, suggesting subordinance of hyenas to male leopards may be mitigated by human disturbance. Furthermore, young male leopards shifted their activity patterns to be more diurnal in response to hyena presence, suggesting that dominance relationship between hyenas and leopards develops with age and is probably related to body size. These results indicate that human disturbance has the potential to affect the competitive relationship between leopards and hyenas in the Udzungwa Mountains, but that relationships will vary with sex and body size.