Vaezi played for Paykan Tehran F.C. before moving to Persepolis F.C. in 2006 on a 2-year deal. Earlier that year he was involved in a drug abuse scandal which ended in a 6-month ban from football and the breakdown of a transfer to F.C. Zob Ahan. Eventually he signed for Persepolis F.C.
Vaezi made his debut for Iran in a friendly match against Georgia in August 2000. He was called up to join the squad in a few occasions, including in 2007, but did not make any other appearance for Team Melli before January 2008, when he made his second cap in a friendly match against Qatar.