This study explores how global university rankings incentivize institutions to prioritize bibliometric indicators at the expense of research integrity. Analyzing 98 fast-growing universities, we identified 18 with sharp declines in first and corresponding authorship roles, an early warning sign of potential metric manipulation. These institutions additionally exhibited unusually high publication surges in STEM fields, dense co-authorship networks, reciprocal citation behavior, and rising rates of self-citations, retractions, and publications in delisted journals. To assess these risks globally, the author developed the Research Integrity Risk Index (RI²), a composite profiling metric combining retraction rates and reliance on delisted journals into a single score and ranking. The index effectively identifies institutions with atypical research performance patterns that deviate from global norms, highlighting systemic vulnerabilities in current evaluation frameworks. The findings underscore the need to rethink how research performance is measured to safeguard academic integrity and mitigate gaming behaviors.