During plant invasions, exotic species have to face new environmental challenges and are affected by interacting components of global change, which may include more stressful environmental conditions. We investigated an invasive species of New Zealand grasslands, commonly exposed to two concomitant and limiting abiotic factors—high levels of ultraviolet-B radiation and drought. The extent to which Verbascum thapsus may respond to these interacting stress factors via adaptive responses was assessed in a greenhouse experiment comprising native German plants and plants of exotic New Zealand origins. Plants from both origins were grown within four treatments resulting from the crossed combinations of two levels of UV-B and drought. Over twelve weeks, we recorded growth, morphological characteristics, physiological responses and productivity. The results showed that drought stress had the strongest effect on biomass, morphology and physiology. Significant effects of UV-B radiation were restricted to variables of leaf morphology and physiology. We found neither evidence for additive effects of UV-B and drought nor origin-dependent stress responses that would indicate local adaptation of native or exotic populations. We conclude that drought-resistant plant species might be predisposed to handle high UV-B levels, but emphasize the importance of setting comparable magnitudes in stress levels when testing experimentally for antagonistic interaction effects between two manipulated factors.