Large Language Models (LLMs) are often quantized to lower precision to reduce the memory cost and latency in inference. However, quantization often degrades model performance, thus fine-tuning is required for various downstream tasks. Traditional fine-tuning methods such as stochastic gradient descent and Adam optimization require backpropagation, which is error-prone in the low-precision settings. To overcome these limitations, we propose the Quantized Zeroth-Order (QuZO) framework, specifically designed for fine-tuning LLMs through low-precision (e.g., 4- or 8-bit) forward passes. Our method avoids the low-precision straight-through estimator, which requires backward computation, and instead utilizes optimized stochastic rounding to mitigate increased bias. QuZO simplifies the training process, while achieving results comparable to first-order methods in rm FP8 and superior accuracy in rm INT8 and rm INT4 training. Experiments demonstrate that QuZO achieves competitive performance on classification, multi-choice, and generation tasks under low-bit training, including zero-shot reasoning tasks. Notably, QuZO incurs minimal overhead and reduces memory consumption by 2.94 times–5.47 times compared to quantized first-order methods during LLaMA-7B fine-tuning.