Interspecific competition can strongly influence the evolutionary response of a species to a changing environment, impacting the chance that the species survives or goes extinct. Previous work has shown that when two species compete for a temporally shifting resource distribution, the species lagging behind the resource peak is the first to go extinct due to competitive exclusion. However, this work assumed symmetrically distributed resources and competition. Asymmetries can generate differences between species in population sizes, genetic variation and trait means. We show that asymmetric resource availability or competition can facilitate coexistence and even occasionally cause the leading species to go extinct first. Surprisingly, we also find cases where traits evolve in the opposite direction to the changing environment because of a ‘vacuum of competitive release’ created when the lagging species declines in number. Thus, the species exhibiting the slowest rate of trait evolution is not always the most likely to go extinct in a changing environment. Our results demonstrate that the extent to which species appear to be tracking environmental change and the extent to which they are preadapted to that change may not necessarily determine which species will be the winners and which will be the losers in a rapidly changing world.