Global environmental change not only entails changes in mean environmental conditions but also in their variability. Changes in climate variability are often associated with altered disturbance regimes and temporal patterns of resource availability. Here we show that increased variability of soil nutrients strongly promotes another key process of global change, plant invasion. In experimental plant communities, the success of one of the world's most invasive plants, Japanese knotweed, is two- to four-fold increased if extra nutrients are not supplied uniformly, but in a single large pulse, or in multiple pulses of different magnitudes. The superior ability to take advantage of variable environments may be a key mechanism of knotweed dominance, and possibly many other plant invaders. Our study demonstrates that increased nutrient variability can promote plant invasion, and that changes in environmental variability may interact with other global change processes and thereby substantially accelerate ecological change.