Instruction-tuned large language models (LLMs) exhibit strong instruction-following and generalization abilities, enabled by expensive post-training pipelines. However, adapting them to specific downstream tasks remains challenging: direct fine-tuning often disrupts this delicate balance, while existing adapter-based transfer methods typically treat the instruction-tuned model as a passive target that only participates at the final merging stage. We propose GIFT (Guided Fine-Tuning and Transfer), a simple and efficient framework that incorporates instruction-level guidance into task adaptation. GIFT fine-tunes a low-rank adapter on the pretrained base model using token-level confidence signals derived from the instruction-tuned model. The learned adapter is then merged into the instruction-tuned model, yielding task-specialized models that preserve general instruction-following behavior. We evaluate GIFT on mathematical reasoning and knowledge-intensive benchmarks across multiple model families and scales. Results show that GIFT consistently outperforms direct fine-tuning and representative transfer-based baselines, while maintaining robust generalization and favorable test-time scaling behavior.