Organizational teams frequently come into conflict with one another over limited resources. Core theories of intergroup conflict suggest that such inter-team resource conflicts unite teams internally, reducing intra-team power struggles. However, conflict spill-over theory suggests that inter-team conflicts may also stimulate competitive power dynamics within teams. We reconcile these two opposing lines of thought by introducing the internal power structure of teams as the key moderator that determines whether inter-team conflict reduces or promotes power struggles within teams. We theorize that while the common fate of members of egalitarian teams makes them likely to unite and pool resources when facing an inter-team conflict, the power differences in hierarchical teams cause members to be differently impacted by the resource-threatening inter-team conflict, leading them to have different perspectives and concerns, thereby promoting internal fights over resources (i.e., power struggles). In turn, such power struggles are expected to negatively affect team performance. We tested these hypotheses with a laboratory study of 85 three-person negotiation teams and a field study of 158 organizational work teams, and find, as expected, that a resource-threatening inter-team conflict promotes performance-detracting power struggles in hierarchical (but not egalitarian) teams.