Inference constitutes the majority of costs throughout the lifecycle of a large language model (LLM). While numerous LLM inference engines focusing primarily on low-level optimizations have been developed, there is a scarcity of non-intrusive client-side frameworks that perform high-level optimizations. In this paper, we introduce Cache Saver, a modular, plug-and-play, and asynchronous framework that facilitates high-level inference optimizations, thereby integrating cleanly into existing systems without requiring changes to the end-user application logic or the underlying LLM. The key novelty is a *namespace-aware list-valued cache* that ensures *statistical integrity* of LLM responses by generating *i.i.d.* responses within a namespace as well as ensuring *reproducibility*. Moreover, as a direct consequence of operating at a high level, Cache Saver supports both local and online models. We conduct extensive experiments with five representative state-of-the-art reasoning strategies, five diverse benchmark tasks, and three different LLMs. On average across all methods, tasks, and LLMs, Cache Saver reduces cost by ≃ 25% and CO₂ by ≃ 35%. Notably, Cache Saver excels in practical machine learning scenarios such as benchmarking across multiple methods or conducting ablation analysis of a specific method, obtaining substantial cost and carbon footprint reduction of ≃ 60%. Cache Saver is publicly available at [https://github.com/au-clan/cachesaver](https://github.com/au-clan/cachesaver).