The biggest win of Sutton's career – and his only major championship – came a year later at the 1983 PGA Championship. He entered into a long drought shortly thereafter, going from 1986 to 1995 without a PGA Tour victory. He nearly lost his tour card late in the string, maintaining it only by using a one-time-only exemption for players in the top 50 of the all-time PGA Tour career money list. After this disappointing eight years, Sutton rejuvenated his career in 1995 with a win at the B.C. Open.
Sutton ranked in the top 10 of the Official World Golf Rankings for over 50 weeks from their debut in 1986 to 1987 and then again for over 50 weeks between 1999 and 2001. He has reached the top five of the rankings.
After playing on four U.S. Ryder Cup teams (1985, 1987, 1999, 2002), he was named non-playing captain of the team for 2004. The competition, played at Oakland Hills Country Club, saw Europe beat the USA by 18.5 points to 9.5 points. Inevitably, Sutton came in for some criticism of his performance as captain, especially for his decision to pair Tiger Woods with Phil Mickelson on the first day of play.
In 2007 he received the Payne Stewart Award. He won it for his charitable efforts which include the establishment of the Christus Schumpert Sutton Children's Hospital in his hometown of Shreveport, Louisiana. He also teamed up with Louisianans Kelly Gibson and David Toms to raise more than $2 million in aid to Hurricane Katrina and Hurricane Rita victims. Sutton was also awarded the Omar N. Bradley Spirit of Independence Award in 2004 and the Golf Writers Association of America's 2006 Charlie Bartlett Award with Gibson and Toms for their relief efforts.