This left Vedenin with one more race: the 4x10km relay.
Four years earlier, at the 1968 Winter Olympics, Vedenin had anchored the Soviet relay team and missed a bronze medal when Finland's Eero Mäntyranta passed him just as they reached the finish line. He went on to win a silver medal in the 50km competition. In Sapporo, Vedenin was again chosen to be the Soviet anchor. This time he took over 61½ seconds behind Johs Harviken of Norway. Vedenin gradually closed the gap, overtook Harviken one kilometre from the finish, and went on to win by just slightly more than 9 seconds.