This study examines international brain race for world-class universities as measured by the QS World University Rankings (QS) and the Academic Ranking of World Universities, particularly in the context of Asian nations' institutional competition and benchmarking against American counterparts. Applying mixed methods with statistical analysis of time-series data from 59 nations and case study of four selected nations, the study examines the cross-national trends of global university rankings and the roles of government policies during the era of performance-driven accountability in higher education. Tracking the zero-sum game of global university rankings over the past decade, the study accounts for key driving factors that produced divergent trajectories among the nations: how and why the USA as established leader and Japan as early catch-up leader become losers, whereas China and Korea as fast followers become winners? Although the Asian catch-up model of world-class university development, high-stakes institutional competitions and targeted funding with STEM priorities contributed to their rapid growth of research productivity and rankings, it reveals major limitations and problems. Drawing cross-national lessons and implications, we discuss new directions of higher education policies and global university ranking measures.