Taymazov later moved to Uzbekistan, but his goal remained the same.
On Saturday night, he finally became a three-time Olympic champion -- just like Karelin.
Taymazov won his third straight gold medal in the men's 120-kg division, beating Georgia's Davit Modzmanashvili to become the third male wrestler to win golds in three consecutive Olympics -- along with Karelin and Alexander Medved of the former Soviet Union.
By virtue of his silver in Sydney in 2000, Taymazov also equaled Karelin's Olympic medal haul in Greco-Roman wrestling. He quickly acknowledged that Karelin should still be ranked higher because he's won more world championships.
"He's the name in wrestling, and I'm really, really glad that I've equalized with him on the medal total," Taymazov said.
"I wanted to be like [Karelin], and now I am."
Two Azerbaijanis -- Toghrul Asgarov and Sharif Sharifov -- also won gold medals Saturday.
Asgarov won the gold medal in the men's 60-kilogram freestyle, upsetting Besik Kudukhov of Russia 1-0, 5-0.
Asgarov, the 19-year-old junior world champion from 2011, beat Coleman Scott of the United States in the semifinals of the men's 60-kilogram freestyle before taking down Kudukhov, the four-time world champion, in the final.
Kudukhov settled for bronze in Beijing and silver in London, while Scott recovered to win bronze for the U.S.
Scott made a surprise run to the semis before being drubbed by Asgarov.
Jake Herbert's first loss had U.S. wrestling coach Zeke Jones going after officials. Jones was given a yellow card as a warning after a challenge by the U.S. resulted in Sharifov being awarded the victory in the second period.
Scott is the unlikeliest medal winner yet for the Americans. His bronze also meant that the U.S. wrestlers wouldn't come home with just one medal, the way they did in Beijing.
"It wasn't the medal I wanted, but I couldn't leave with nothing. I would not be denied a medal," Scott said.