Superionic lithium conductivity has only been discovered in a few classes of materials, mostly found in thiophosphates and rarely in oxides. Herein, we reveal that corner-sharing connectivity of the oxide crystal structure framework promotes superionic conductivity, which we rationalize from the distorted lithium environment and reduced interaction between lithium and non-lithium cations. By performing a high-throughput search for materials with this feature, we discover ten new oxide frameworks predicted to exhibit superionic conductivity-from which we experimentally demonstrate LiGa(SeO₃)₂ with a bulk ionic conductivity of 0.11 mS cm^-1 and an activation energy of 0.17 eV. Our findings provide insight into the factors that govern fast lithium mobility in oxide materials and will accelerate the development of new oxide electrolytes for all-solid-state batteries.