Avilov has trained at the Odessa youth sports school #5 affiliated with the Ukrainian republican administration of the Soviet Dynamo. Since 1964 he was in the national team of the Ukrainian SSR.
He won a gold medal in the 1972 Summer Olympics decathlon with a new world record of 8454 points. He returned to win a bronze medal (8369 points) in the 1976 Summer Olympics. A near seven foot high jumper, he was one of the few great Soviet athletes of Jewish heritage.