Noted for his swinging stride, Golubnichy set his first 20-kilometre world record of 1 h 30 min 2.8 sec when he was 19 years old. At the 1960 Olympic Games in Rome, he braved heat, humidity, and persistent challengers to win the walk by just nine seconds, with a time of 1 h 34 min 7.2 sec. After winning a bronze medal in the 1964 Olympics at Tokyo, he returned to the Games in 1968 in Mexico City and held off a furious late challenge by José Pedraza of Mexico to win by only three yards, clocking in at 1 h 33 min 58.4 sec. Golubnichy then finished a close second in the 1972 Munich Olympics and made his final Olympic appearance, at the age of 40, in Montreal, finishing seventh.

Golubnichy also won medals at the European championships, finishing third in 1962, second in 1966, and first in 1974. His best 20-kilometre walk was timed at 1 h 23 min 55 sec in 1976.