This paper investigates the effect of university prestige stratification on scholars' career achievements. We focus on 766 STEM PhD graduates hired by Mexican universities between 1992 and 2016. We rank university according to their prestige based on the pairwise assessment of quality contained in the PhD hiring networks. Further, we use a quasi-experimental design matching pairs of individuals with the same characteristics, PhD training or first job experience. Our results challenge the positive association between prestige and academic performance as predicted by the 'Matthew effect'. Scholars hired internally sustain higher performance over their careers in comparison to those who move up or down the prestige hierarchy. Further, we find a positive (negative) relation between downward (upward) prestige mobility and performance that relates to the "big-fish-little-pond" effect (BFLPE). The evidence of a BFLPE-like effect has policy implications because hinders the knowledge flows throughout the science system and individual achievements.