Dominance relationships between females and males are characteristic traits of species and are usually associated with sexual dimorphism. Exploring the social and contextual circumstances in which females win conflicts against males allows one to study the conditions triggering shifting power asymmetries between the sexes. This study investigates dominance relationships in bonobos (Pan paniscus), a species in which females are thought to display social dominance despite male-biased sexual dimorphism. To identify dominance relationships among females and males, we first explored how intrasexual dominance status affects the outcome of intersexual conflicts. Second, by incorporating social and behavioral information about the context of intersexual conflicts, we tested to which extent different components of power are relevant to the observed asymmetries in the relationships. Post-hoc analyses indicate a sex-independent dominance hierarchy with several females occupying the top ranks. Our results also reveal that two factors—female leverage and motivation to help offspring—had a significant influence on the outcome of intersexual conflicts. The results of our study do not indicate an overall reduction in male aggression against females but do show lower levels of male aggression in the mating context, and an absence of male aggression toward those females displaying visual signs of elevated fecundity. This indicates that both female sexuality and male mating strategies are involved in the shifting dominance relationships between the sexes.