Quantization is widely adopted to accelerate inference and reduce memory consumption in large language models (LLMs). While activation-weight joint quantization enables efficient low-precision decoding, it suffers substantial performance degradation on multi-step reasoning tasks. We propose QSPEC, a novel quantization paradigm that decouples efficiency from quality by integrating two complementary schemes via speculative decoding: low-precision joint quantization for fast drafting and high-precision weight-only quantization for accurate verification. QSPEC reuses both weights and KV cache across stages, enabling near-zero-cost switching without retraining or auxiliary models. Compared to high-precision baselines, QSPEC achieves up to 1.64x speedup without quality degradation, and outperforms state-of-the-art speculative decoding methods by up to 1.55x in batched settings. Furthermore, QSPEC supports plug-and-play deployment and generalizes well across model scales, quantization methods, and workloads. These properties make QSPEC a practical and scalable solution for high-fidelity quantized LLM serving under memory-constrained scenarios.