Kelly was drafted by the Seattle Pilots in the 8th round of the 1968 Major League Baseball Draft. After three unspectacular years in the Pilots/Milwaukee Brewers organization, he was given his unconditional release on 6 April 1971. On 28 April 1971, Kelly was signed as a minor league free agent by the Twins and sent to the AA Charlotte Hornets in the South Atlantic League. From 1972 through 1975, Kelly would spend most of his playing time at AAA Tacoma Twins in the Pacific Coast League, splitting time between first base and the corner outfield positions. After starting the 1975 season again in Tacoma, Kelly was called up to the big club and would make his major league debut on 11 May 1975. Kelly would play in 49 games with the Twins over the 1975 season while seeing playing time at first base and the outfield. Prior to the start of the 1976 season, Kelly was purchased from the Twins by the Baltimore Orioles and assigned to Rochester Red Wings; he would not return to the major leagues. In 1977, he returned to the Twins organization and AAA Tacoma - this time as a player-manager. In 1978, Kelly played for the Twins new AAA affiliate, the Toledo Mudhens, spending his last year as a full-time player.
Following the 1978 season, Kelly was sent down to manage the Twins A-affiliate, the Visalia Oaks in the California League, staying there through the 1980 season. After taking a year off, Kelly was named the manager of the Twins AA affiliate, the Orlando Twins, for the 1982 season. In 1983, Kelly was added to manager Billy Gardner's big-league coaching staff where he would remain until being named Twins manager during the 1986 season. Kelly was the 11th manager of the team and his tenure as manager was the longest in team history. Under his tenure, the Twins won two World Series crowns in the span of five years (1987 and 1991); however, from 1994 to 1997 a long sequence of retirements and injuries (including superstars Kent Hrbek and Kirby Puckett) hurt the team badly, and Kelly spent the remainder of his managerial career rebuilding the Twins.
In 1998, management cleared out the team of all of its players earning over 1 million dollars (except for pitcher Brad Radke) and rebuilt from the ground up; the team went 70–92 and in fourth place in the AL Central, 19 games behind the Cleveland Indians and five games ahead of the Detroit Tigers. A run of eight consecutive losing seasons ended in 2001, when the Twins led the division for much of the year before fading, finishing at 85–77, second to Cleveland. He then resigned at age 51, citing burnout, and the threat of contraction. Kelly was succeeded as manager of the Twins by Ron Gardenhire, and his rebuilding efforts paid off the year after he retired from the Twins, with a repeat of divisional championships in 2002, 2003, and 2004.
The Minnesota Twins announced on January 26, 2012 that they would retire Tom Kelly's jersey number, No. 10, before a September 8, 2012 game.
A year after taking over the reins of the Twins from Ray Miller, Kelly took the team that he had helped build through his role as one of the top people in the Twins' minor league organization and led it to a World Series championship. Though the '87 Twins were criticized for being the top team in a weak division (amassing only a .525 record in regular season play, which was the worst winning percentage for an eventual World Champion until surpassed by the St. Louis Cardinals in 2006), they easily handled the Detroit Tigers in five games, losing only Game 3 of the American League Championship Series to a heartbreaking 8th-inning two-run home run.
The World Series was a well-fought contest between the Twins and the National League champion St. Louis Cardinals, each team winning all of its home games. Games 1, 2, 4 and 6 were decidedly lopsided contests (10–1 Twins, 8–4 Twins, 7–2 Cards, 11–5 Twins), with Games 3, 5 and 7 being much closer contests, each being decided by only two runs (3–1 Cards, 4–2 Cards and 4–2 Twins).
After a 63-year drought, Tom Kelly's leadership helped propel the Twins to their second World Championship (the first coming in 1924 as the Washington Senators).
Following two closely contested victories at home, the Twins traveled to Atlanta where they suffered three straight defeats. Tom Kelly, prior to the Series' move to Atlanta, infamously suggested that managing without the designated hitter was "right up there with rocket science". Although he was being facetious, the grueling Game 3 proved Kelly prescient as a series of double switches and substitutions emptied the Twins' bench and both teams' bullpens. Kelly was forced to pinch hit Rick Aguilera in the top of the twelfth and was prepared to send outfielder Dan Gladden to the mound if necessary; however, the Braves won in the bottom of the twelfth when David Justice narrowly beat a throw to the plate. After a similarly close Game 4 and a dominating 14–5 Braves victory in Game 5, the Twins had to win the final two games at home.
Game 6 featured two climactic plays by Kirby Puckett who, in the top of the 3rd, made a sensational leaping catch against the center field acrylic glass to prevent a Braves' run. The Twins won 4–3 in the bottom of the 11th when Puckett blasted a home run off Charlie Leibrandt. Game 7 proved to be one of the greatest games in baseball history, as the game remained scoreless for 9 innings and included a number of decisive and memorable plays. Twins starter Jack Morris argued repeatedly with Kelly to allow him to stay in the game and pitched 10 scoreless innings before the Twins won in the bottom of the 10th, giving Minnesota its second World Series victory in five years.