Sandhi, the phonological merging of morphemes, is a central feature of Sanskrit grammar. While Sandhi formation is well-defined by Pāṇini’s Aṣṭādhyāyī, the reverse task—Sandhi splitting—is substantially more complex due to inherent ambiguity and context-sensitive transformations. Accurate splitting is a critical precursor to tokenization in Sanskrit, which lacks explicit word boundaries and presents densely fused compounds. In this work, we present a data-driven approach, fine-tuning the Gemma-3 4B large language model on a dataset of over 49,000 training and 2,000 test examples of compound words and their morpheme-level decompositions. Leveraging the Unsloth framework with low-rank adaptation (LoRA) and 4-bit quantization, we train the model to predict these splits. Our work yields a scalable, Sandhi-aware system designed to enhance modern NLP pipelines for classical Sanskrit, demonstrating an effective application of LLMs to this linguistic challenge.