Daraselia was born to a Georgian father and Abkhaz mother on 9 January 1957. His birth date was later changed by Soviet sports officials to 9 October 1957 so that he could play longer for the national junior team. Daraselia also played for FC Dinamo Tbilisi and Soviet Union senior national team. He scored a winning goal for FC Dinamo Tbilisi in 1981, in the final game of the UEFA Cup Winners' Cup, rushing into the penalty area past two defenders, just 3 minutes before the full-time whistle.