Encroachment of woody plants into arid and semi-arid grasslands is well-documented. Effects on nutrient cycles and community composition are profound but it remains unclear why some native shrubs have spread dramatically while others have not. We suggest that the capacity for rapid taproot elongation by seedlings under a wide range of moisture conditions is associated with encroachment potential. To test this hypothesis we compared seedling emergence and growth of two species with different encroachment histories in southern Arizona: Acacia greggii (not an encroacher) and Prosopis velutina (a strong encroacher). Seedlings were grown in a controlled environment for 2.5 weeks, varying the number of watering days to trigger germination (“trigger duration”; 4 levels) and the follow-up watering frequency (2 levels). We hypothesized that taproot elongation would be faster in P. velutina (H₁) and that P. velutina would be more responsive to water inputs both during (H₂) and after (H₃) germination. Evidence supporting H₁ was weak and there was no support for H₃. However, there was strong support for H₂: taproot elongation increased linearly with trigger duration with a slope 43% higher in P. velutina than A. gregii (P = 0.0093). This suggests that newly emerged P. velutina seedlings are highly responsive to the magnitude of the rainfall event which triggers germination, thus reducing the time until seedlings can escape (a) topsoil desiccation and (b) strong below-ground competition from shallow-rooted competitors, such as grasses. By contrast, A. greggii seems less able to take advantage of rainfall early in the growing season.