Abstract: We utilize the universality of pion--pion (ππ) final-state interactions at small invariant masses to understand their enhanced localized CP violation in B±→K±π+π−, using a dispersive approach. From a fit to the integrated CP-asymmetry data, we successfully predict the Dalitz-plot kinematic distribution of the asymmetry in the low-energy ππ region, including the large localized CP violation recently observed by LHCb. An essential role is played by the contributions of isospin 2. This formalism, whose parameters have a physical meaning, can be adapted straightforwardly to other systems with CP violation enhanced by final-state interactions.