Natural communities are incredibly diverse, and explaining how this biodiversity is even possible remains a central question in ecology. Resource competition is thought to play an important role in community interactions, but understanding diverse communities using resource competition is limited by the competitive exclusion principle: the prediction that only as many species as resources should coexist. Here, we demonstrate that sequential resource utilization, also known as diauxie, under periodic growth and death cycles allows for many more coexisting species than resources, violating the competitive exclusion principle. These violations become possible when fluctuations produce variations in the resource depletion order on each growth cycle. The depletion order varying allows the community to experience different sequences of temporal niches on each growth cycle, with temporal niches being the increasingly depleted environments produced by sequential resource depletions. While community-driven fluctuations and competitive-exclusion violations are rare under constant environmental conditions, we find that with even small environmental fluctuations most communities violate competitive exclusion, with several times as many survivors as resources in some simulations. We explore the competitive interactions within these communities and show that survivors are accurately predicted by temporal niches. We thus demonstrate highly diverse communities as a likely outcome of resource competition with a competitive structure based on ordered resource preferences.