Zeroth-order (ZO) optimization is a memory-efficient alternative to backpropagation for fine-tuning large language models, but its deployment is limited by the high variance of gradient estimation. We propose **GRZO**, a **G**roup-**R**elative **Z**eroth-**O**rder optimizer that draws one pseudo-independent perturbation per mini-batch example and aggregates the per-example losses through group-relative normalization, raising the effective gradient-direction count from one to the batch size at no additional forward cost while preserving inference-level memory. We prove that GRZO is directionally unbiased with variance shrinking proportionally to the batch size, yielding a tighter nonconvex convergence bound than MeZO. Across RoBERTa-large, Llama3-8B, and OPT-13B over multiple tasks, GRZO improves average accuracy on Llama3-8B by +3.0 over MeZO while staying within 0.5% of the forward-only inference memory floor; as a drop-in replacement for the MeZO core, it lifts sparse, low-rank, and quantized ZO variants by +4.9 on average.