Rust has made safe systems programming practical on the CPU, but writing custom GPU kernels in Rust still forces programmers outside the language's ownership guarantees. We present cuTile Rust, a tile-based system for safe, idiomatic GPU kernel authoring in Rust. cuTile Rust extends Rust's ownership discipline to tile-based GPU kernels: mutable outputs are split into disjoint pieces, kernel launches preserve the host-side ownership contract, and programmers can opt out locally when they need lower-level control. The system also provides a composable host execution model spanning synchronous launches, asynchronous pipelines, and CUDA graph replay. Our evaluation shows that these abstractions can preserve performance on high-end GPUs. On the NVIDIA B200 GPU, cuTile Rust achieves 7 TB/s for element-wise operations and 2 PFlop/s for GEMM (96% of cuBLAS), matching cuTile Python within measurement noise. Grout, a cuTile-Rust-based inference engine, exercises cuTile Rust across an end-to-end Qwen3 inference path. In batch-1 decode, Grout reaches 171 generated tokens/s for Qwen3-4B on the NVIDIA GeForce RTX 5090 and 82 generated tokens/s for Qwen3-32B on the B200, competitive with vLLM and SGLang and consistent with an HBM roofline sanity check.