Sorting is a foundational primitive in modern data processing, influencing the execution speed of high-performance data pipelines. However, the algorithmic landscape is currently bifurcated by a pervasive "Stability Tax": practitioners must sacrifice either order preservation for high throughput or execution speed for stability. To address these limitations, this paper introduces, zSort, an adaptive z-score based distribution sorting algorithm that guarantees stability while avoiding pass complexity that scales with key-width. The performance of the proposed technique is evaluated using Microarchitectural analysis and experimental results. Microarchitectural analysis shows that zSort achieves a lower bad-speculation overhead (19.7%) than both stable baselines and several high-performance unstable algorithms and sustains a competitive IPC of 1.44. Empirical evaluation across diverse input distributions and datasets of up to 10^7 elements (64 bit) demonstrates that zSort consistently outperforms widely used comparison based stable sorting algorithms, achieving up to 3x-4.5x speedups, and a relatively better performance compared to LSD Radix, with larger gains on duplicate heavy and partially ordered inputs. Despite providing stability, zSort achieves comparable throughput as compared to high-performance unstable algorithms such as Skasort. It also maintains this performance on adaptive workloads where methods like Pdqsort typically excel and doesn't exhibit any extreme worst case. These results indicate that zSort substantially narrows the traditional performance gap between stable and unstable sorting and provides an efficient, stable sorting alternative.