As global changes reorganize plant communities, invasive plants may benefit. We hypothesized that elevated CO2 and warming would strongly influence invasive species success in a semi‐arid grassland, as a result of both direct and water‐mediated indirect effects. To test this hypothesis, we transplanted the invasive forb Linaria dalmatica into mixed‐grass prairie treated with free‐air CO2 enrichment and infrared warming, and followed survival, growth, and reproduction over 4 yr. We also measured leaf gas exchange and carbon isotopic composition in L. dalmatica and the dominant native C3 grass Pascopyrum smithii. CO2 enrichment increased L. dalmatica biomass 13‐fold, seed production 32‐fold, and clonal expansion seven‐fold, while warming had little effect on L. dalmatica biomass or reproduction. Elevated CO2 decreased stomatal conductance in P. smithii, contributing to higher soil water, but not in L. dalmatica. Elevated CO2 also strongly increased L. dalmatica photosynthesis (87% versus 23% in P. smithii), as a result of both enhanced carbon supply and increased soil water. More broadly, rapid growth and less conservative water use may allow invasive species to take advantage of both carbon fertilization and water savings under elevated CO2. Water‐limited ecosystems may therefore be particularly vulnerable to invasion as CO2 increases.