Between 1961 and 1972 he won eight tournaments on the PGA Tour. He won the Canadian PGA Championship five times, and won the World Cup with Al Balding in 1968. He wrote a book, The Natural Golf Swing (ISBN 0-7710-4534-4) with Lorne Rubenstein.
Knudson tied for second in the 1969 Masters, one shot behind champion George Archer. In seven Masters appearances, Knudson posted three top-10s, including 10th in his 1965 debut and sixth a year later.
He was inducted into Canada's Sports Hall of Fame in 1969.
Knudson left tournament golf in the late 1970s, and started teaching golf, with success, at a facility in the Toronto area. His teaching methods have since been adopted by the Canadian PGA.
In 1988 he was inducted into both Royal Canadian Golf Association Hall of Fame, the Manitoba Sports Hall of Fame and Museum and was made a member of the Order of Canada.
He was diagnosed with lung cancer in 1988. He recovered, and was about to make a comeback at the Liberty Mutual Legends of Golf Senior tournament, but left because he felt weak. The cancer had spread to his brain, and he would die from it in 1989.
He was buried at Mount Pleasant Cemetery in Toronto, Ontario.