While prompt optimization has emerged as a critical technique for enhancing language model performance, existing approaches primarily focus on elicitation-based strategies that search for optimal prompts to activate models' capabilities. These methods exhibit fundamental limitations when addressing knowledge-intensive tasks, as they operate within static knowledge capacity rather than providing the factual knowledge, terminology precision, and reasoning patterns required in specialized domains. To address these limitations, we propose Knowledge-Provision-based Prompt Optimization (KPPO), a framework that reformulates prompt optimization as systematic knowledge integration rather than potential elicitation. KPPO introduces three key innovations: 1) a knowledge gap filling mechanism for knowledge gap identification and targeted remediation; 2) a batch-wise candidate evaluation approach that considers both performance improvement and distributional stability; 3) an adaptive knowledge pruning strategy that balances performance and token efficiency, reducing up to 29% of inference token usage. Evaluation on 15 knowledge-intensive benchmarks from various domains demonstrates KPPO's superiority over elicitation-based methods, with an average improvement of ~6% over baselines while achieving comparable or lower token consumption.