The tunable band gaps and facile fabrication of perovskites make them attractive for multi-junction photovoltaics1,2. However, light-induced phase segregation limits their efficiency and stability3-5: this occurs in wide band gap (> 1.65 eV) I/Br mixed perovskite absorbers, and becomes even more acute in the top cells of triple-junction solar photovoltaics that requires a fully 2.0 eV band gap absorber2,6. We report herein that lattice distortion in I/Br mixed perovskites is correlated with the suppression of phase segregation, generating an increased ion migration energy barrier arising from the decreased average interatomic distance between A-site cation and iodide. Using a ~2.0 eV Rb/Cs mixed-cation inorganic perovskite with large lattice distortion in the top subcell, we fabricated all-perovskite triple-junction solar cells and achieved an efficiency of 24.3% (23.3% certified quasi-steady-state efficiency) with an open-circuit voltage of 3.21 V. This is, to our knowledge, the first reported certified efficiency for perovskite-based triple-junction solar cells. The triple-junction devices retain 80% of their initial efficiency following 420 hours of operation at the maximum power point.