Identifying how dominance within and between the sexes is established is pivotal to understanding sexual selection and sexual conflict. In many species, members of one sex dominate those of the other in one-on-one interactions. Whether this results from a disparity in intrinsic attributes, such as strength and aggressiveness, or in extrinsic factors, such as social support, is currently unknown. We assessed the effects of both mechanisms on dominance in the spotted hyaena (Crocuta crocuta), a species where sexual size dimorphism is low and females often dominate males. We found that individuals with greater potential social support dominated one-on-one interactions in all social contexts, irrespective of their body mass and sex. Female dominance emerged from a disparity in social support in favour of females. This disparity was a direct consequence of male-biased dispersal and the disruptive effect of dispersal on social bonds. Accordingly, the degree of female dominance varied with the demographic and kin structure of the social groups, ranging from male and female co-dominance to complete female dominance. Our study shows that social support can drive sex-biased dominance and provides empirical evidence that a sex-role-defining trait can emerge without the direct effect of sex.