The increasing amount of pressure related to water and energy shortages has increased the urgency of cultivating individual conservation behaviors. While the concept of nudging, i.e., providing usage-based feedback, has shown promise in encouraging conservation behaviors, its efficacy is often constrained by the lack of targeted and actionable content. This study investigates the impact of the use of large language models (LLMs) to provide tailored conservation suggestions for conservation intentions and their rationale. Through a survey experiment with 1,515 university participants, we compare three virtual nudging scenarios: no nudging, traditional nudging with usage statistics, and LLM-powered nudging with usage statistics and personalized conservation suggestions. The results of statistical analyses and causal forest modeling reveal that nudging led to an increase in conservation intentions among 86.9%-98.0% of the participants. LLM-powered nudging achieved a maximum increase of 18.0% in conservation intentions, surpassing traditional nudging by 88.6%. Furthermore, structural equation modeling results reveal that exposure to LLM-powered nudges enhances self-efficacy and outcome expectations while diminishing dependence on social norms, thereby increasing intrinsic motivation to conserve. These findings highlight the transformative potential of LLMs in promoting individual water and energy conservation, representing a new frontier in the design of sustainable behavioral interventions and resource management.