We report the discovery of superconductivity at a pressure-induced magnetic quantum phase transition in the Kondo lattice system CeSb_{2}, sustained up to magnetic fields that exceed the conventional Pauli limit eightfold. Like CeRh_{2}As_{2}, CeSb_{2} is locally noncentrosymmetric around the Ce site, but the evolution of critical fields and normal state properties as CeSb_{2} is tuned through the quantum phase transition motivates a fundamentally different explanation for its resilience to applied field.