Brago won his first Soviet title in 1951 with the coxed fours and was selected to represented his country in the eights at the 1952 Helsinki Games, where he won a silver medal. He had even more success at the European Championships, taking gold three consecutive times from 1953 through 1955. Domestically, the remainder of his titles were in the eights as well, as he took them from 1952-1954 and in 1956.
Brago was also an accomplished academic, first graduating from the Moscow Energy Institute in 1953 and earning his doctoral degree in 1979. He later worked in academia in the field of automation and also served in several administrative positions.