Multivariate adaptation to climatic shifts may be limited by trait integration that causes genetic variation to be low in the direction of selection. However, strong episodes of selection induced by extreme climatic pressures may facilitate future population‐wide responses if selection reduces trait integration and increases adaptive potential (i.e., evolvability). We explain this counter‐intuitive framework for extreme climatic events in which directional selection leads to increased evolvability and exemplify its use in a case study. We tested this hypothesis in two populations of the lizard Anolis scriptus that experienced hurricane‐induced selection on limb traits. We surveyed populations immediately before and after the hurricane as well as the offspring of post‐hurricane survivors, allowing us to estimate both selection and response to selection on key functional traits: forelimb length, hindlimb length, and toepad area. The direct selection was parallel in both islands and strong in several limb traits. Even though overall limb integration did not change after the hurricane, both populations showed a non‐significant tendency toward increased evolvability after the hurricane despite the direction of selection not being aligned with the axis of most variance (i.e., body size). The population with comparably lower between‐limb integration showed a less constrained response to selection. Hurricane‐induced selection, not aligned with the pattern of high trait correlations, likely conflicts with selection occurring during normal ecological conditions that favours functional coordination between limb traits, and would likely need to be very strong and more persistent to elicit a greater change in trait integration and evolvability. Future tests of this hypothesis should use G‐matrices in a variety of wild organisms experiencing selection due to extreme climatic events.