Large Language Model (LLM) inference is rapidly becoming a core datacenter service, yet current serving stacks keep the host CPU on the critical path for orchestration and token-level control. This makes LLM performance sensitive to CPU interference, undermining application colocation and forcing operators to reserve CPU headroom, leaving substantial capacity unutilized. We introduce Blink, an end-to-end serving architecture that removes the host CPU from the steady-state inference path by redistributing responsibilities across a SmartNIC and a GPU. Blink offloads request handling to the SmartNIC, which delivers inputs directly into GPU memory via RDMA, and replaces host-driven scheduling with a persistent GPU kernel that performs batching, scheduling, and KV-cache management without CPU involvement. Evaluated against TensorRT-LLM, vLLM, and SGLang, Blink outperforms all baselines even in isolation, reducing pre-saturation P99 TTFT by up to 8.47$\times$ and P99 TPOT by up to 3.40$\times$, improving decode throughput by up to 2.1$\times$, and reducing energy per token by up to 48.6$\%$. Under CPU interference, Blink maintains stable performance, while existing systems degrade by up to two orders of magnitude.