The rapid growth of large language models (LLMs) has made GPU communication a critical bottleneck. While prior work reduces communication volume via quantization or lossy compression, these approaches introduce numerical errors that can degrade convergence, accuracy, and stability. We present UCCL-Zip, a unified design that integrates lossless compression directly into GPU communication primitives. UCCL-Zip supports both point-to-point (P2P) and collective communication without modifying user-facing APIs or compromising numerical correctness. For P2P communication, Uzip-P2P employs a split-send pipeline that exposes transmissible data early and overlaps compression with communication, while preserving high GPU efficiency by operating on large data blocks. For collective communication, Uzip-NCCL integrates compression into NCCL's persistent kernel model via fused execution, eliminating redundant memory traffic and kernel launches. In real workloads, UCCL-Zip accelerates RL weight synchronization by up to 47.5% and reduces vLLM end-to-end inference latency by up to 10%, all without application changes.