In 1958, Knutsen won Nordic combined in the Holmenkollen Ski Festival; he was the only Norwegian to win an event. That year, he also came 9th at the FIS Nordic World Ski Championships 1958. He won the national titles in 1959 and 1960. In 1960, he also placed second in ski jumping at the national championships. He was a favourite for the Nordic combined event at the 1960 Winter Olympics, and finished second to Georg Thoma. After placing fourth at the FIS Nordic World Ski Championships 1962, he won the national title in 1963 and 1964. Knutsen won a gold medal in the Nordic combined event at the 1964 Winter Olympics in Innsbruck, Austria. He had been in second place, behind Thoma, after the ski jumping phase of the event. It was Norway's first gold medal of the Games. Later in the year, Knutsen finished sixth at the Holmenkollen Ski Festival, and he retired at the end of the 1964 season. In 1964, he wrote an autobiography "I hopp og løype" ("In jumps and trails").