Large Language Models (LLMs) have revolutionized the ability to understand and generate text, enabling significant progress in automatic knowledge graph construction from text (Text2KG). Many Text2KG methods, however, rely on iterative LLM prompting, making them computationally expensive and prone to overlooking complex relations distributed throughout the text. To address these limitations, we propose InvertiTune, a framework that combines a controlled data generation pipeline with supervised fine-tuning (SFT). Within this framework, the data-generation pipeline systematically extracts subgraphs from large knowledge bases, applies noise filtering, and leverages LLMs to generate corresponding natural text descriptions, a task more aligned with LLM capabilities than direct KG generation from text. This pipeline enables generating datasets composed of longer texts paired with larger KGs that better reflect real-world scenarios compared to existing benchmarks, thus supporting effective SFT of lightweight models for single-shot KG construction. Experimental results on CE12k, a dataset generated using the introduced pipeline, show that InvertiTune outperforms larger non-fine-tuned LLMs as well as state-of-the-art Text2KG approaches, while also demonstrating stronger cross-dataset generalization on CrossEval-1200, a test set created from three established benchmark datasets and CE12k. These findings highlight the importance of realistic, high-quality training data for advancing efficient and high-performing Text2KG systems.