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Prompt tuning adapts Vision-Language Models like CLIP to open-world tasks with minimal training costs. In this direction, one typical paradigm evaluates model performance **separately** on known classes (*i.e.*, base domain) and unseen classes (*i.e.*, new domain). However, real-world scenarios require models to handle inputs **without prior domain knowledge**. This practical challenge has spurred the development of **open-world prompt tuning**, which demands a unified evaluation of two stages: 1) detecting whether an input belongs to the base or new domain (**P1**), and 2) classifying the sample into its correct class (**P2**). What's more, as domain distributions are generally unknown, a proper metric should be insensitive to varying base/new sample ratios (**P3**). However, we find that current metrics, including HM, overall accuracy, and AUROC, fail to satisfy these three properties simultaneously. To bridge this gap, we propose $\mathsf{OpenworldAUC}$, a unified metric that jointly assesses detection and classification through pairwise instance comparisons. To optimize $\mathsf{OpenworldAUC}$ effectively, we introduce **Gated Mixture-of-Prompts (GMoP)**, which employs domain-specific prompts and a gating mechanism to dynamically balance detection and classification. Theoretical guarantees ensure generalization of GMoP under practical conditions. Experiments on 15 benchmarks in open-world scenarios show GMoP achieves SOTA performance on $\mathsf{OpenworldAUC}$ and other metrics.