Offline reinforcement learning (RL) enables training from fixed data without online interaction, but policies learned offline often struggle when deployed in dynamic environments due to distributional shift and unreliable value estimates on unseen state-action pairs. We introduce Behavior-Adaptive Q-Learning (BAQ), a framework designed to enable a smooth and reliable transition from offline to online RL. The key idea is to leverage an implicit behavioral model derived from offline data to provide a behavior-consistency signal during online fine-tuning. BAQ incorporates a dual-objective loss that (i) aligns the online policy toward the offline behavior when uncertainty is high, and (ii) gradually relaxes this constraint as more confident online experience is accumulated. This adaptive mechanism reduces error propagation from out-of-distribution estimates, stabilizes early online updates, and accelerates adaptation to new scenarios. Across standard benchmarks, BAQ consistently outperforms prior offline-to-online RL approaches, achieving faster recovery, improved robustness, and higher overall performance. Our results demonstrate that implicit behavior adaptation is a principled and practical solution for reliable real-world policy deployment.