Safety alignment—training large language models (LLMs) to refuse harmful requests while remaining helpful—is critical for responsible deployment. Prior work established that safety behaviors are governed by low-rank structures, suggesting parameter-efficient fine-tuning (PEFT) should be well-suited for alignment. However, Low-Rank Adaptation (LoRA) consistently underperforms full fine-tuning and reinforcement learning on safety benchmarks. We attribute this gap to semantic entanglement: safety-relevant directions are intertwined with unrelated concepts due to polysemanticity, impeding implicit subspace identification. To address this, we propose SAILS (Safety Alignment via Interpretable Low-rank Subspace), which leverages Sparse Autoencoders (SAEs) to disentangle representations into monosemantic features, constructs an interpretable safety subspace from SAE decoder directions, and uses it to initialize LoRA adapters. Theoretically, we prove that SAE-based identification achieves arbitrarily small recovery error under monosemanticity assumptions, while direct identification suffers an irreducible error floor. Empirically, SAILS achieves up to 99.6% safety rates across multiple model families and scales, exceeding full fine-tuning and matching RLHF-based models, with only 0.2% of parameters updated and providing interpretability.