Corbin played collegiately at DePaul University from 1981 to 1985. He played in 120 games for the Blue Demons, increasing his scoring average and field goal and free throw percentage in each of his four seasons. Corbin posted averages of 11.5 points (on .504 FG and .764 FT), 7.4 rebounds, 1.9 assists, 1.1 steal and 2.3 turnovers in 31.1 minutes per game. He finished seventh on DePaul's career scoring list and was a two-time honorable mention AP All-America selection, as well as an All-NIT choice in 1983, and he was invited to the 1984 Olympic trials. He graduated with a degree in computer science, before becoming a second-round pick of the San Antonio Spurs in the 1985 NBA Draft. He was a team captain in his junior and senior years; the former was Ray Meyer's last as head coach, the latter was Joey Meyer's first. He was inducted into the DePaul University Athletics Hall of Fame in 2005.
Corbin played in the NBA at small forward from 1985 to 2000. His first two seasons were with the San Antonio Spurs, as he was their selection in the second round (35th pick overall) of the 1985 NBA Draft. After signing with the Cleveland Cavaliers in January 1987, he was part of the trade by the Cavs which sent Kevin Johnson, Mark West, 1988 first- and second-round draft picks and a 1989 second-round draft pick to the Phoenix Suns for Larry Nance, Mike Sanders and a 1988 first-round draft choice in February 1988. After being selected by the Minnesota Timberwolves in the expansion draft in 1989, he led the team and established career-highs in 1989-90 in rebounds (7.4) and steals (2.13). Corbin also recorded the first triple-double in Timberwolves history, with 10 points, 13 rebounds and a career-high 10 assists, against the Dallas Mavericks on January 2, 1991. His stint with the Jazz came by a trade with the Minnesota Timberwolves for Thurl Bailey early in the 1991-92 season, enabling him to help the team reach the NBA Western Conference Finals twice. He averaged 9.6 points and 6.2 rebounds in 233 games for the Jazz from 1991 to 1994. He was then traded by the Jazz with a 1995 second-round draft pick to the Atlanta Hawks for Adam Keefe in September 1994. It was in Atlanta where his streak of 415 consecutive games played would be broken. Corbin then was traded to the Sacramento Kings for Spud Webb in June 1995. Along with Walt Williams, he went to the Miami Heat for Billy Owens and Kevin Gamble in February 1996. He then spent three seasons with the Hawks via free-agent signing in 1996. After returning to the Kings as a free agent in 1999, he spent the next season with the Toronto Raptors. He was traded by Toronto with Corliss Williamson, Kornel David and a first-round draft pick to the Detroit Pistons for Jerome Williams and Eric Montross in February 2001. Wearing No. 23 and No. 33 throughout his playing career, he averaged 9.3 points (on .457 percent from the field), 4.8 rebounds, 1.8 assists and 1.2 steals in nearly 26 minutes per game while playing 1,065 games in his career. A versatile small forward, Corbin also played in 81 NBA playoff games in his career, including 37 with the Jazz, averaging 8.4 points and 5.0 rebounds per game.
After his playing career, Corbin spent two seasons with the Charleston Lowgators of the NBDL as a player mentor. Corbin was hired by Scott Layden, then general manager of the New York Knicks, as manager of Knicks player development for the 2003-04 season. In 2004, he went to the Utah Jazz, spending seven years as an assistant coach under Jerry Sloan before eventually succeeding Sloan as head coach in 2011.
On April 21, 2014, the Jazz announced that they had elected not to offer Corbin a new contract. Afterwards he became an assistant coach of the Sacramento Kings and on December 15, 2014 he was promoted to interim head coach after Mike Malone was fired.