Maximum Inner Product Search (MIPS) for high-dimensional vectors is pivotal across databases, information retrieval, and artificial intelligence. Existing methods either reduce MIPS to Nearest Neighbor Search (NNS) while suffering from harmful vector space transformations, or attempt to tackle MIPS directly but struggle to mitigate redundant computations due to the absence of the triangle inequality. This paper presents a novel theoretical framework that equates MIPS with NNS without requiring space transformation, thereby allowing us to leverage advanced graph-based indices for NNS and efficient edge pruning strategies, significantly reducing unnecessary computations. Despite a strong baseline set by our theoretical analysis, we identify and address two persistent challenges to further refine our method: the introduction of the Proximity Graph with Spherical Pathway (PSP), designed to mitigate the issue of MIPS solutions clustering around large-norm vectors, and the implementation of Adaptive Early Termination (AET), which efficiently curtails the excessive exploration once an accuracy bottleneck is reached. Extensive experiments reveal the superiority of our method over existing state-of-the-art techniques in search efficiency, scalability, and practical applicability. Compared with state-of-the-art graph based methods, it achieves an average 35% speed-up in query processing and a 3x reduction in index size. Notably, our approach has been validated and deployed in the search engines of Shopee, a well-known online shopping platform. Our code and an industrial-scale dataset for offline evaluation will also be released to address the absence of e-commerce data in public benchmarks.