Invasion success of species introduced to novel environments may be facilitated by adaptive evolution and by phenotypic plasticity. Here we investigate the independent and joint contribution of both mechanisms as drivers of invasiveness in the perennial sunflower Helianthus tuberosus. We show that invasive genotypes have multiple origins, and that invasive spread was facilitated by the repeated evolution of extreme values in a single trait, clonality. In line with genetic accommodation theory, we establish that this evolutionary transition occurred by refining a preexisting plastic response of clonality to water availability. Further, we demonstrate that under the non-drought conditions typically experienced by this plant in its introduced range, invasive spread is mediated by hybrid vigour and/or two major additive-effect loci, and that these mechanisms are complementary. Thus, in H. tuberosus, evolution of invasiveness was facilitated by phenotypic plasticity, and involved the use of multiple genetic solutions to achieve the same invasiveness trait.