While Large Language Models (LLMs) excel in high-resource contexts, reasoning capabilities in low-resource languages (LRLs) like Sindhi remain limited. To bridge this gap, we introduce Sindhi-Reasoning-Instruct, the first culturally grounded Sindhi instruction corpus. We fine-tuned six LLaMA and Mistral models (1B–24B) to evaluate if parameter-efficient tuning enables deductive, inductive, and causal reasoning. Results demonstrate that linguistically authentic data is the decisive factor. Fine-tuning effectively restored Sindhi’s Perso-Arabic orthography and SOV structure, with the Mistral-Small-24B model achieving a massive 141% relative improvement in human quality ratings over its base version. Furthermore, structured reasoning capabilities were found to scale with model size; while smaller models achieved high fluency, Mistral-Small-24B achieved top performance across logical categories, reaching 83% on inductive reasoning tasks. This study provides empirical evidence that expert-curated, native instruction data allows LRL models to move beyond simple translation toward robust, structured reasoning. The dataset and models are publicly available.