A top prize at the 1971 Herbert von Karajan Competition catapulted him to the highest circle of Soviet artistry.
Conducting for more than one hundred concerts a year, he regularly toured the USSR, collaborating with musicians such as David and Igor Oistrakh, Leonid Kogan, Dmitri Shostakovich, Kiril Kondrashin, and Emil Gilels.
He defected to the West by being driven across the Finnish-Swedish border in Haaparanta to Luleå, Sweden, and on to Stockholm by Jyrki Koulumies, a Finnish journalist.
For two days they sat under false names in a safehouse room, not even daring to go outside because their photographs were on the front page of every Swedish and international newspaper.
Immediately after his defection, Jordania made his Carnegie Hall debut, which was described by the New York Times as "a confident and spirited performance ... the full house leaped to its feet."
Jordania's homeland, the Republic of Georgia, bestowed on him the highest award given to outstanding Georgians, the Ordin of Honor.
Jordania regularly conducted at many prestigious opera houses in Russia, the United States, Ukraine, and South Korea, including the Bolshoi and Kirov Theaters.