In June 2001 Vescovi won the South American Chess Championship (FIDE 2.4 Zonal). This victory qualified him to play in the FIDE World Chess Championship, which started in November. Here he was knocked out in the second round by Veselin Topalov. In 2003, he tied with Alexander Goldin for first place in the American Continental Chess Championship in Buenos Aires, placing second on tiebreak. This result qualified him for the FIDE World Chess Championship 2004, where he was eliminated in the first round by Gadir Guseinov.