Jones became the Indians' full-time closer by 1988, breaking the Indians' record for saves in a season with 37. He held the Indians' all-time record for saves with 129 until Bob Wickman broke it on May 7, 2006.
Jones announced his retirement on December 7, 2000. His 303 career saves ranked 12th in major league history upon his retirement, and his 846 career appearances ranked 21st. A changeup specialist, he was known for keeping hitters off balance by throwing extremely slow pitches. He threw a two-seam fastball that topped out in the low to mid 80's and a knuckle curve on occasion.
He was elected to the American League All-Star team three times (1988, 1989 and 1990) and to the National League All-Star team twice (1992 and 1994). He was the oldest player in the majors in 2000 at the age of 43.