An exotic species can be a superior colonizer but inferior resource competitor relative to native species. Such species can spatially coexist for an extended period of time in a community maintained via competition-colonization (CC) trade-offs. Whether fluctuations in resource supply allow such exotic species to successfully invade and displace the native species or hold the coexistence is not previously explored, and it is the focus of this study. In this article, we model propagule-limited spatial competition explicitly linked with resource-competition within the framework of the classic CC-model, while time-dependent fluctuations in resource supply are considered in a sinusoidal function. The model predicts that if the amplitude of the fluctuations is greater than the average resource supply rate, there exist a range of values of fluctuation frequency that can allow the exotic species to successfully invade the habitat and to reduce the extent of native species. On the other hand, if the fluctuation amplitude is less than the average resource supply rate, such exotic species can coexist with the native species, independent of fluctuation frequencies. In addition, we found that at a constant resource supply rate, the exotic species can stably coexist with the native species at competitive equilibrium.