Goalby enjoyed a lengthy and successful career on the PGA Tour, collecting 14 tournament victories, including the 1968 Masters Tournament, and second-place finishes at the 1961 U.S. Open and the 1962 PGA Championship. Goalby set the PGA Tour record for consecutive birdies after he collected eight during the 1961 St. Petersburg Open. He was also selected to the 1963 Ryder Cup team, compiling a 3-1-1 record. Goalby remained active in golf following his playing days, serving as an analyst for NBC Sports for 14 years. He later became a founding member of the popular Senior PGA Tour, and served 11 years on the Senior Tour's policy board.