Introgressive hybridization is a process that enables gene flow across species barriers through the backcrossing of hybrids into a parent population. This may make genetic material, potentially including relevant environmental adaptations, rapidly available in a gene pool. Consequently, it has been postulated to be an important mechanism for enabling evolutionary rescue, that is the recovery of threatened populations through rapid evolutionary adaptation to novel environments. However, predicting the likelihood of such evolutionary rescue for individual species remains challenging. Here, we use the example of Zosterops silvanus, an endangered East African highland bird species suffering from severe habitat loss and fragmentation, to investigate whether hybridization with its congener Zosterops flavilateralis might enable evolutionary rescue of its Taita Hills population. To do so, we employ an empirically parameterized individual-based model to simulate the species' behaviour, physiology and genetics. We test the population's response to different assumptions of mating behaviour and multiple scenarios of habitat change. We show that as long as hybridization does take place, evolutionary rescue of Z. silvanus is likely. Intermediate hybridization rates enable the greatest long-term population growth, due to trade-offs between adaptive and maladaptive introgressed alleles. Habitat change did not have a strong effect on population growth rates, as Z. silvanus is a strong disperser and landscape configuration is therefore not the limiting factor for hybridization. Our results show that targeted gene flow may be a promising avenue to help accelerate the adaptation of endangered species to novel environments, and demonstrate how to combine empirical research and mechanistic modelling to deliver species-specific predictions for conservation planning.