The founding population in most new species introductions, or at the leading edge of an ongoing invasion, is likely to be small. Severe Allee effects-reductions in individual fitness at low population density-may then result in a failure of the species to colonize, even if the habitat could support a much larger population. Using a simulation model for plant populations that incorporates demography, mating systems, quantitative genetics, and pollinators, we show that Allee effects can potentially be overcome by transient hybridization with a resident species or an earlier colonizer. This mechanism does not require the invocation of adaptive changes usually attributed to invasions following hybridization. We verify our result in a case study of sequential invasions by two plant species where the outcrosser Cakile maritima has replaced an earlier, inbreeding, colonizer Cakile edentula (Brassicaceae). Observed historical rates of replacement are consistent with model predictions from hybrid-alleviated Allee effects in outcrossers, although other causes cannot be ruled out.