Many introduced plants pose invasion risks globally and threaten the biodiversity of native ecosystems. Such non-native plants can become invasive when they have advantages over native plants, such as having fewer natural enemies. Invasive plants often have the ability to alter ecosystem properties after they have become established, which can make it difficult to eliminate the invasive. In principle, this can cause a regime shift that may not be reversed through intense control efforts that increase mortality and reduce growth of the invasive species. Here we use spatially explicit agent-based modeling to simulate the invasion of an introduced tree species into a habitat occupied by a native species. The model describes an invasive tree with fast growth and high seed production and, in addition, produces litter that has a suppressive effect on native seedlings. These are properties, for example, shared by the invasive Melaleuca quinquenervia in southern Florida habitats. We use simulation modeling to test the following logical hypotheses: Partial suppression of native tree seedlings by the invasive tree's litter (1) will accelerate the spread of the invasive tree into native vegetation, (2) will impede efforts to control invasive spread through biocontrol, and (3) can cause a regime shift that is not reversed even if the biocontrol lowers invasive growth and reproduction to levels substantially lower than those of the native species. Additionally, (4) the earlier in the invasion biocontrol is introduced, the more effective it will be in reversing the invasion. The simulations support all four hypotheses. While these results highlight the potential for biocontrol of invasive tree species, our findings also suggest that successful elimination of positive litter feedbacks and invasive spread may critically depend on the timing of control efforts within the invasion process.